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# /sci/ - Science & Math

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No.11101083 [Reply] [Original] [archived.moe]

>just starting making up random shit
>literally call it imaginary
Wow, math is so pure...

 >> Anonymous Mon Oct 28 23:39:10 2019 No.11101100 >>11101083can't solvex^3-5x+1=0without imaginary numberseven though all three solutions arenormal real numbershttps://www.google.com/search?q=y=x^3-5x%2B1https://youtu.be/_qvp9a1x2UM?t=3m
 >> Anonymous Mon Oct 28 23:42:56 2019 No.11101115 >>11101083>Math is all made upStop the press!
 >> Anonymous Mon Oct 28 23:48:45 2019 No.11101139 >>11101083>Lets sort all things with "x" property together and name it>>But what about those things who do not have that property?>Lets call them something else>>OMG YOU'RE JUST MAKING SHIT UPYeah but who cares?
 >> Anonymous Mon Oct 28 23:52:31 2019 No.11101156 >>11101083Complex numbers are just an elegant way of extending the 1D real number line to the 2D Argand PlaneYou could achieve the same results with 2D vectors, but it wouldn't be as aesthetically pleasing
 >> Anonymous Mon Oct 28 23:55:33 2019 No.11101165 >>11101083x^2 = -1sqrt(y)^2 = -1y^2/2 = -1sqrt(-1)^2 = -1what's wrong with this?
 >> Anonymous Tue Oct 29 00:00:57 2019 No.11101187 >dudes what if square root, right..? >but... square root... of negative one..!>>"Can't do that little nigga. Negative numbers don't have a square root.">yea bu->>"nigga... no."imagine how much simpler things would be if there was always a real nigga around to keep things real.
 >> Anonymous Tue Oct 29 00:02:39 2019 No.11101194 >>11101187A lot harder. Try writing sin(17x) in terms of only sin(x) and cos(x) without complex numbers.
 >> Anonymous Tue Oct 29 00:06:47 2019 No.11101208 >>11101194There are no complex parts about it. Sin and cos are used relative to geometry and angles, which necessitates a 2d graphing plane. imaginary-i is functionally just the y plane on an xy graph.the y-axis would remain to exist without i
 >> Anonymous Tue Oct 29 00:11:13 2019 No.11101226 >>11101208Then fucking do it, retard.
 >> Anonymous Tue Oct 29 00:15:04 2019 No.11101246 $\displaystyle\\ z_1 = x_1+y_1i \; \; \; \; \; z_2 = x_2+y_2i\\ z_1^* = x_1-y_1i \; \; \; \; \; z_2^* = x_2-y_2i\\ | z_1 | = \sqrt{x_1^2+y_1^2} \; \; \; \; \; | z_2 | = \sqrt{x_2^2+y_2^2}\\ z_1+z_2 = x_1+x_2 + (y_1+y_2)i\\ \left | z_1+z_2 \right |^2 = \left ( \sqrt{(x_1+x_2)^2+(y_1+y_2)^2} \right ) ^2 = (x_1+x_2)^2 +(y_1+y_2)^2\\ z_1z_2^* = x_1x_2 -x_1y_2i +y_1ix_2 -y_1iy_2i = x_1x_2+y_1y_2 +(x_2y_1-x_1y_2)i\\ z_1^*z_2 = x_1x_2 +x_1y_2i -y_1ix_2 -y_1iy_2i = x_1x_2+y_1y_2 +(x_1y_2-x_2y_1)i\\ z_1z_2^* + z_1^*z_2 = 2(x_1x_2+y_1y_2) = \text{2Re}(z_1z_2^*) = \text{2Re}(z_1^*z_2)\\ |z_1|^2+|z_2|^2 + z_1z_2^* + z_1^*z_2 = x_1^2+y_1^2 + x_2^2 + y_2^2 + 2(x_1x_2+y_1y_2)\\ = (x_1^2 + 2x_1x_2 + x_2^2) + (y_1^2 + 2y_1y_2 + y_2^2) = (x_1+x_2)^2 +(y_1+y_2)^2$
 >> Anonymous Tue Oct 29 00:27:12 2019 No.11101296 >>11101083Why does this thread exist? sage, reported, cringe and bluepilled, kys, dilate, etc.
 >> Anonymous Tue Oct 29 00:54:55 2019 No.11101375 File: 126 KB, 1131x622, 1541774512917.jpg [View same] [iqdb] [saucenao] [google] [report] nooo bros nonononono the 300k noooooooo
 >> Anonymous Tue Oct 29 00:57:08 2019 No.11101378 >>11101375based
 >> Anonymous Tue Oct 29 00:57:08 2019 No.11101379 >>11101375|1+i|=sqrt(2)
 >> Anonymous Tue Oct 29 01:02:01 2019 No.11101390 >>11101375My favourite part of this is the fact that he placed an image in the speech bubble.
 >> Anonymous Tue Oct 29 01:12:51 2019 No.11101408 >observe something, make massive assumption that observation even occurred as remembered in the first place>ignore that same set of conditions that were first observed can never exist again under any circumstances>claim to see "same" set of condition again>enough people make the same claim, now its Fact™Wow, the sciences are so rigorous and grounded in reality, not like that phony math...
 >> El Arcón Tue Oct 29 01:29:55 2019 No.11101436   File: 89 KB, 500x500, TIMESAND___iuwtef7sef76276276276272tef9t2efg.jpg [View same] [iqdb] [saucenao] [google] [report] yeah
 >> Anonymous Tue Oct 29 01:32:57 2019 No.11101444 >>11101100Its called solving by substitution and it works perfectly without complex numbers. You can't get a closed nice formula.
 >> Anonymous Tue Oct 29 01:43:35 2019 No.11101469 >>11101083Just curious. Can a quaternion be a complex root to a certain polynomial? Or even an octonion?
 >> Anonymous Tue Oct 29 01:43:39 2019 No.11101470 >>11101156No, you're missing the point. You don't multiply and divide 2D vectors
 >> Anonymous Tue Oct 29 01:46:27 2019 No.11101474 >>11101469If the polynomial has only complex coefficients, no.
 >> Anonymous Tue Oct 29 02:23:51 2019 No.11101545 >>11101444>Rube Goldberg machine mathfound the engineer
 >> Anonymous Tue Oct 29 02:25:57 2019 No.11101551 >>11101436it follows directly from inf's definition:-unbounded-larger than any number
 >> Anonymous Tue Oct 29 02:36:11 2019 No.11101565 File: 35 KB, 480x360, complex.jpg [View same] [iqdb] [saucenao] [google] [report] >>11101083"imaginary" is the most unfortunate misnomer in math. calculations based on these "imaginary" quantities reliably predict real-world phenomena
 >> Anonymous Tue Oct 29 03:15:34 2019 No.11101651 >>11101565When you spend years formulating the mathematics to explain 3d physics that fully capture the mathematical elegance of what is going on in the world. But everyone is a brainlet so they go with vectors instead and all they give you is your I j k notation and make fun of imaginary numbers
 >> Anonymous Tue Oct 29 03:19:15 2019 No.11101658 File: 92 KB, 640x768, William_Rowan_Hamilton_painting3.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Tue Oct 29 03:19:57 2019 No.11101660 >>11101651What are you even trying to make fun of?
 >> Anonymous Tue Oct 29 03:58:46 2019 No.11101716 >>11101660The picture of Hamilton didnt upload for some reason even though I included it. Its Hamilton. Learn your math history.
 >> Anonymous Tue Oct 29 03:59:50 2019 No.11101718 >>11101565Phasor diagrams actually make the analysis really easy
 >> Anonymous Tue Oct 29 04:00:54 2019 No.11101723 >>11101083Pic is wrong. i^2 = -1, yes, but there's no such thing as square roots of negative numbers.
 >> Anonymous Tue Oct 29 04:12:42 2019 No.11101739 >>11101083Nothing wrong with imaginary numbers, they're well defined and self consistent. Reals on the other hand...
 >> Anonymous Tue Oct 29 04:14:10 2019 No.11101740 >>11101723At this point I can't tell if this is a joke or not
 >> Anonymous Tue Oct 29 04:14:19 2019 No.11101742 >>11101565can someone explain how this works, i mean how do imaginary numbers predict real world stuff
 >> Anonymous Tue Oct 29 04:26:38 2019 No.11101758 >>11101742Rotations. Instead of saying "90 degrees" or "120 degrees," you say $e^{i\frac{\pi}{2}}$ and $e^{i\frac{2\pi}{3}}$. Calculations are then done with exponentials, in a way that's unambiguous** and mathematically rigorous>**mathfags don't seem to get this
 >> Anonymous Tue Oct 29 04:26:58 2019 No.11101761 >>11101742Real world stuff involves differential equations with time derivatives. If we do a Fourier transform that derivative becomes multiplication by a frequency and i. So rather than thinking about differential equations we can just do algebra with complex numbers
 >> Anonymous Tue Oct 29 04:42:21 2019 No.11101779 >>11101740not. it's a popsci sloppy meme
 >> Anonymous Tue Oct 29 04:45:48 2019 No.11101783 >>11101083If imaginary numbers are 2 dimensional, what would be 3 dimensional numbers be? How do you even get into 3rd axis? Because square root of i is still on complex 2d plane
 >> Anonymous Tue Oct 29 04:48:30 2019 No.11101785
 >> Anonymous Tue Oct 29 04:52:09 2019 No.11101792 File: 18 KB, 360x360, sILE1Lk_d.jpg [View same] [iqdb] [saucenao] [google] [report] >>11101783>Hasn't heard of sedenions.>Hasn't heard of quaternions.
 >> Anonymous Tue Oct 29 05:11:46 2019 No.11101819 >>11101083You're actually retarded
 >> Sol i Vagus/Sindy Vagus Tue Oct 29 05:16:26 2019 No.11101824 >>11101083So all of Euler is essentially a mathematical sort that says: "Irrationals+Negatives belong on the left, Variables/Exponents/Negatives/Iterants/Directions belong on the right."
 >> Anonymous Tue Oct 29 05:18:42 2019 No.11101826 >>11101779>>11101740You both don't understand imaginary numbers. Roots of imaginary numbers have infinite solutions. In order to make them unique, their domain is restricted to the cut imaginary plane, the cut being exactly on the negative real numbers.https://math.stackexchange.com/questions/44406/how-do-i-get-the-square-root-of-a-complex-numberThe absolute state of /sci/...
 >> Anonymous Tue Oct 29 05:22:31 2019 No.11101833 >>11101083complex numbers represent rotations and uniform scalings. -1 is the rotation by 180 degrees (or a point reflection through the origin). the equation x^2 = -1 literally says "what do you need to do twice to get rotation by 180 degrees?" that's right motherfuckes, rotation by 90 or 270 degrees. that's i and -i.
 >> Sol i Vagus/Sindy Vagus Tue Oct 29 05:23:32 2019 No.11101837 File: 567 KB, 445x875, 6ba.png [View same] [iqdb] [saucenao] [google] [report] >>11101833Hey! My right is YOUR left! FANCY THAT!
 >> Anonymous Tue Oct 29 05:38:09 2019 No.11101853 >>11101826>In order to make them unique, their domain is restricted to the cut imaginary planeArbitrary bullshit.And from your link,>What's the rational basis for having positive square roots as the principal square roots instead of negative square roots?I still haven't heard a good answer for this>>11101833Hot take: negative numbers are undefined in the complex plane
 >> Anonymous Tue Oct 29 05:40:42 2019 No.11101855 >>11101853>arbitrary bullshitSo are your ramblings. You seem to have never heard a math lecture before. What's the third root of -8?
 >> Anonymous Tue Oct 29 05:47:40 2019 No.11101869 >>11101855>What's the third root of -8?It depends.
 >> Sol i Vagus/Sindy Vagus Tue Oct 29 05:50:09 2019 No.11101873 >>11101869>On how much we get paid, fellow Jew. Kekek number manipulation.
 >> Anonymous Tue Oct 29 06:06:36 2019 No.11101894 >>11101758>>11101761so imaginary numbers are just a trick to (ironically) avoid complexity and make our calculations easier e.g. instead of degrees we use exponentials like anon saidas far as real world stuff cares its all same from their perspective
 >> Anonymous Tue Oct 29 06:15:45 2019 No.11101915 >>11101742Do you know about Power in circuits? How P = VI?Now, a motor, for example, has an apparent power, which in mathematics is given by:S = VI*, I* being the complex conjugate of the phasor I. Now, S, the apparent power, is:S = P + iQP = True Power(what your motor gives or drains in reality).Q = Reactive power(not real, it just to account for things like Capacitor and inductor that DOESN'T dissipate power, but still drops voltage and draw current)Yet, you can use things in real world to calculate the Reactive power and you want it to be low as possible(because if you fix S and you low Q, that means your P, the true power, increase and that is ALWAYS good). Reactive power is an example of what is a complex number that can be calculated in the real world.Reactive power keeps circulating around your circuit from machine to machine and so on.
 >> Anonymous Tue Oct 29 06:26:40 2019 No.11101931 >>11101915thank you anonyes im familiar with those things back from high school of electrical engineeringexcept nobody ever explained us the real world correlationit was always like, this is how things go, learn it and gtfo
 >> Anonymous Tue Oct 29 06:33:11 2019 No.11101933 >>11101758seriouslytry doing AC circuit analysis, literally most of quantum mechanics without complex numbers...The amount of trig functions would make you go insane.
 >> Anonymous Tue Oct 29 06:41:51 2019 No.11101945 >>11101933so is this correct thinking >>11101894
 >> Anonymous Tue Oct 29 07:31:47 2019 No.11102008 >>11101945well sure but I think many academics also see complex numbers and the complex plane as an actual mathematical/physical structure that nature is taking advantage of. It's simply wonderful that you can add arguments of multiplying exponents. Doing calculations in the complex plane enough and rotations become second nature. admittedly it's been a few years for me.
 >> Anonymous Tue Oct 29 07:46:55 2019 No.11102021 think of 'i' as a placeholderwe'll fill our equation with i's, shuffle things around, and then at the end we multiply them all out again.
 >> Anonymous Tue Oct 29 08:57:12 2019 No.11102096 >>11101083Holy shit are you underage or just trolling? Also, the image is wrong, but I won't even bother telling you why.
 >> Anonymous Tue Oct 29 09:57:03 2019 No.11102209 >>11101869Not really, no.
 >> Anonymous Tue Oct 29 10:01:59 2019 No.11102218 >>11101853>>What's the rational basis for having positive square roots as the principal square roots instead of negative square roots?there's none>Hot take: negative numbers are undefined in the complex planethey are
 >> Anonymous Tue Oct 29 10:05:08 2019 No.11102224 >>11102218The rational basis is that it doesn't work for real numbers, so in order not to confuse newfags and brainlets it would be better to shun roots of negative numbers. But sure, any cut does the trick. Whelp, here it happened anyway.
 >> Anonymous Tue Oct 29 10:09:11 2019 No.11102231 >>11101083>>just starting making up random shitThat's actually exactly how math works. You make up random shit and figure out what properties it has.Then when you know its properties you may realize wow, this I can use this random shit to describe some real world stuffs.
 >> Anonymous Tue Oct 29 10:14:46 2019 No.11102238 >>11102224Actually I misread a I thought we were talking about complex square roots. I guess with the real square root it makes *some* sense. The map $\mathbb{R}\setminus 0 \to (0,\infty), x \mapsto x^2$ is a homeomorphism on both connected components, so in the first place it's actually possible to choose an inverse defined on the whole codomain (not possible with the complex sqrt). You choose the component including $1$, because it's a distinguished element.
 >> Anonymous Tue Oct 29 10:43:53 2019 No.11102284 >>11101785It's almost split up like musical time. Quarter notes, eighth notes, sixteenth, and thirty second notes.
 >> Anonymous Tue Oct 29 10:49:34 2019 No.11102297 >>11102284>dude powers of 2
 >> Anonymous Tue Oct 29 11:55:10 2019 No.11102411 >>11101083$\mathbb C = \mathbb R[x]/(x^2+1)$$i = x + (x^2+1)$
 >> Anonymous Tue Oct 29 12:01:28 2019 No.11102423 >>11101470Sure complex numbers are equipped with an additional bilinear map.Indeed, this bilinear map is typically interpreted geometrically: as product of the magnitudes rotated to the sum of the arguments.If you want to be pedentic about using linear algebra formalism though, its pretty easy to represent it using ordinary matrix multiplication. All you need is a basis that respects the negative identity:$J^2 = -J$
 >> Anonymous Tue Oct 29 12:59:02 2019 No.11102514 >>11101651>>11101718>misnomer - a wrong or inaccurate use of a name or term.that post isn't saying imaginary numbers are bad, quite the oppositeit's that they were given a really bad name that makes brainlets think of i like it's a magical fantasy unicornthe term "complex" is much better and it would be really nice if people would just stop using "imaginary" altogether
 >> Anonymous Tue Oct 29 13:05:03 2019 No.11102524 File: 212 KB, 1218x1015, 1555024964702.jpg [View same] [iqdb] [saucenao] [google] [report] >>11101894>as far as real world stuff cares its all same from their perspectivephilosophically speaking, all numbers are in your imaginationthe "real world" doesn't "care" about numbersif you think complex numbers are a "trick" because they help us more easily design real-world systems, then you have to also think of real numbers as a "trick"
 >> Anonymous Tue Oct 29 15:00:22 2019 No.11102817 >>11101792He's asking about 3 dimensional, not 4 or 16 dimensional.>>11101783You can invent a 3 dimensional algebra, but it will not be useful, because it must lack some certain properties. It can be proved that the only real finite dimensional normed division algebras are octonions, quaternions, complex numbers, and real numbers.You can have a 3 dimensional algebra, for example just taking $(\mathbb{R}^3,+,\times),$ where $+$ is regular vector addition, and $\times$ is the cross product. Then you have an anti-commutative, non-associative algebra. It is not a division algebra, since any vectors that a parallel give a cross product of zero.The thing to take away here is that you can invent whatever retarded algebra you want with relative ease, but it is not guaranteed to satisfy certain properties that will actually make it useful.
 >> Anonymous Tue Oct 29 15:03:05 2019 No.11102826 >>11102514Imaginary numbers are $i\mathbb{R},$ complex numbers are $\mathbb{C}.$ They are two different sets, and are not interchangeable.
 >> Anonymous Tue Oct 29 15:07:39 2019 No.11102841 >>11101651What’s wrong with vectors to describe the 3D. ME student so honestly curious.
 >> Anonymous Tue Oct 29 15:09:50 2019 No.11102845 >>11102826Confirmed for brainletimaginary numbers are just complex numbers with $\Re{z} = 0$and thus belong to the field $\mathbb{C}$$i\mathbb{R}$ isn't a field because multiplication of two imaginary numbers doesn't result in another imaginary number. Your construction doesn't make sense
 >> Anonymous Tue Oct 29 15:16:19 2019 No.11102859 >>11102845are you literally retarded ? he's completely right
 >> Anonymous Tue Oct 29 15:17:50 2019 No.11102861 >>11102411based and algebrapilled
 >> Anonymous Tue Oct 29 15:18:01 2019 No.11102863 >>11102859Are you?Please tell me: what FIELD is the number 4i a member of.
 >> Anonymous Tue Oct 29 15:18:12 2019 No.11102865 >>11101436Enough! Go make your own website to spread your crackpot theories and wrong proofs. You suck! You're a no-talent piece of shit! Get out! How dare you come down here and shitpost. I've been on this board for 14 years. You're a disgrace! You suck! Who the hell do you think you are? You're any kind of mathematician? Anybody know who you are? Maybe everyone else wants to enjoy actual mathematical discussion. This is one of the most important places in all of internet for maths, who are you? WHO ARE YOU? You miserable, presumptuous, no-talent. You're no mathematician. A mathematician respects the rigour and precision that serves as the foundation for intellectual achievement. You obviously don't have the talent. You don't have enough respect for yourself or other people, or what it is to express yourself in maths or any other form of study. And I'm a Harvard graduate, sucker. You suck. You're a no-talent. If you really had talent, go practice, and then get yourself published, instead of ruining the day for everybody down here. You're a disgrace! You are everything that's gone wrong with this board. You're a self-consumed, no-talent, mediocre piece of shit. And i've earned the right to say it. Okay? In 1975, I collaborated with Erdos on a paper. Who the fuck are you? You're nothing. You are nothing. And you will never be anything. NEVER. How dare you? You miserable mediocre nothing. Shame on you. Your crat stupid little smile. You're wrong. Go practice more. You can't even put together a simple proof. I don't care about your little alternate definitions of infinity which don't prove anything. It doesn't mean you know how to do maths.You're a crank. I'm trained clasically, I'm trained contemporaneously, and you suck.
 >> Anonymous Tue Oct 29 15:18:29 2019 No.11102866 >>11102845Imaginary numbers are not a field, and our definitions for imaginary numbers are identical.
 >> Anonymous Tue Oct 29 15:19:41 2019 No.11102869 File: 62 KB, 362x332, 1571615139722.gif [View same] [iqdb] [saucenao] [google] [report] >>11102865Yikes!
 >> Anonymous Tue Oct 29 15:21:57 2019 No.11102876 >>11102863$\mathbb{C}$
 >> Anonymous Tue Oct 29 15:22:01 2019 No.11102877 >>11102866And yet i is a member of a field called C
 >> Anonymous Tue Oct 29 15:23:07 2019 No.11102882 >>11101651Hamilton has entered the thread.
 >> Anonymous Tue Oct 29 15:23:24 2019 No.11102884 >>11101783>not knowing i, j , k
 >> Anonymous Tue Oct 29 15:23:32 2019 No.11102885 >>11102876Glad you admit it. What what set 4i is also a member of? Guess what set all complex numbers with Re(z)=0 are members of? Guess what set intersects C?
 >> Anonymous Tue Oct 29 15:23:32 2019 No.11102886 >>11102877Your point?
 >> Anonymous Tue Oct 29 15:25:45 2019 No.11102897 >>11102886iR is a subset of C
 >> Anonymous Tue Oct 29 15:26:31 2019 No.11102898 >>11102885I have legit no idea what's your point. tell me exactly what part of>Imaginary numbers are iR,iR, complex numbers are C.C. They are two different sets, and are not interchangeable.seems so wrong to you.
 >> Anonymous Tue Oct 29 15:27:45 2019 No.11102902 >>11102885None of that contradicts >>11102826Seriously, how are you this retarted?
 >> Anonymous Tue Oct 29 15:30:03 2019 No.11102911 >>11102884>Look at me. I learnt something that someone else didnt learnt. Im so smart.
 >> Anonymous Tue Oct 29 15:30:29 2019 No.11102912 >>11102898Saying they "are different sets, not interchangeable" is pedantic and misleading considering one is a subset of the other.
 >> Anonymous Tue Oct 29 15:35:06 2019 No.11102926 >>11102912>It is pedantic and misleading to say that the empty set is different from a non-empty set considering one is a subset of the other.
 >> Anonymous Tue Oct 29 15:36:45 2019 No.11102928 >>11102912>Saying they "are different sets, not interchangeable" is pedantic and misleading considering one is a subset of the other.LMAO are you for real ? either you're a CS student or an undergrad trying to appear smart. there's literally nothing pedantic or misleading on saying that the set of imaginary numbers is distinct from the set of complex numbers. mainly because it's completely correct, and also because it was actually a valid point in the discussion.
 >> Anonymous Tue Oct 29 16:57:42 2019 No.11103040 >>11102826>Imaginary numbers are iR, complex numbers are C. They are two different sets, and are not interchangeable.that's true, and i didn't mean to imply that they are.maybe it's not so for other languages, but in english, "imaginary" has a certain connotation.it'd be nice to see a new name for the imaginary part of the number. i don't know... anti-real numbers? implied numbers? of course i know this is about as useful as "power triangle" or "tau vs pi" discussion.
 >> Anonymous Tue Oct 29 17:06:26 2019 No.11103057 File: 38 KB, 400x400, gaussed.jpg [View same] [iqdb] [saucenao] [google] [report] >>11101083>imaginaryLateral numbers plz.
 >> Anonymous Tue Oct 29 20:22:13 2019 No.11103534 >>11102898sure $i\mathbb{R} \subset \mathbb{C}$My point was that there's no point in distinguishing the concepts of "imaginary" v.s. "complex" numbers because $i\mathbb{R}$ is not closed under multiplication, and is thus not a useful construct in everyday parlance. Any time you would be plausibly working with imaginary number, you're going to be working with complex numbers, ergo its much more useful to conceptually think of them as an element of the field $\mathbb{C}$ unless you're an annoying pedant which is >>11102912point if I understood him correctly
 >> Anonymous Tue Oct 29 21:07:13 2019 No.11103676 >>11103057The best mathematical maniacs wear their pjs and are annoyed by photography. Imagine how pissed this guy was to be conscious and not doing math.
 >> Anonymous Tue Oct 29 21:19:39 2019 No.11103720 >>11102423And that complex structure J is additional structure a generic 2d vector space does not have.I was trying to teach the person I was replying to that the algebraic structure (i.e. your bilinear map) is the entire point. Complex analysis is not just 2D vector calculus
 >> Anonymous Tue Oct 29 21:30:03 2019 No.11103764 >>11101375Incredibly retarded, jesus christ
 >> Anonymous Tue Oct 29 21:35:32 2019 No.11103789 >>11101758If you write complex numbers in exponential form instead of polar form you're a huge faggot and your circuit analysis 101 prof shouldve fucking slapped you [eqn] Z = |r| \angle \theta [/eqn] Its just so goddamn elegant and aesthetic, makes arithmetic absolutely trivial, nothing can compare.
 >> Anonymous Tue Oct 29 21:38:49 2019 No.11103805 >>11103789They are literally two forms of notation to present the exact same two numbers
 >> Anonymous Tue Oct 29 21:40:03 2019 No.11103811 >>11103805I know, but my personally preferred notation is obviously superior to all other possible notations.
 >> Anonymous Tue Oct 29 21:43:51 2019 No.11103829 >>11103789meh, adding two complex numbers using polar is clunky and inelegant
 >> Anonymous Tue Oct 29 21:55:08 2019 No.11103858 >>11102884i and j are the same, j is just i used in electronics instead to make it better distinguishable between I as current and j also known as i as imaginary number.k is wave number.Nothing 3 dimensional
 >> Anonymous Tue Oct 29 21:58:01 2019 No.11103865 >>11102817Thanks for the explanation, anon.
 >> Anonymous Tue Oct 29 23:50:07 2019 No.11104136 >>11101444>>11101545OP is a limit
 >> Anonymous Tue Oct 29 23:58:03 2019 No.11104153 >>11104136I think you meant dimwit
 >> Anonymous Wed Oct 30 00:02:17 2019 No.11104168 >>11101156>muh 2D vectorsThat's a retarded way to think about complex numbers. The right way to think about complex numbers is as the algebraic closure of the real numbers.
 >> Anonymous Wed Oct 30 01:18:20 2019 No.11104363 >>11103858wtf are you talking about you fucking engilearn what quaternions are, pleb
 >> Anonymous Wed Oct 30 01:21:27 2019 No.11104367 >>11101083Actually that first one is not true $i =/= sqrt{-1}[/eqn]  >> Anonymous Wed Oct 30 01:26:26 2019 No.11104376 >>11104367you ducked up your latexis the problem that it isn't +/- i in OP?  >> Anonymous Wed Oct 30 01:29:29 2019 No.11104383 >>11104367>>11104376√ simpliciter denotes the principal square root  >> Anonymous Wed Oct 30 01:32:15 2019 No.11104391 >>11104383can you say that in plain English please. not my first language  >> Anonymous Wed Oct 30 01:36:01 2019 No.11104398 >>11104391By "simpliciter" I mean "without qualification"By principal square root I mean this https://en.wikipedia.org/wiki/Square_root#Principal_square_root_of_a_complex_numberThere are two complex numbers that square to -1, but only one of them is the principal square root of -1  >> Anonymous Wed Oct 30 01:37:48 2019 No.11104406 >>11104383>√ simpliciterwhat's the regular square root look like then>>11104398so is it just that it should have been +/- i?  >> Anonymous Wed Oct 30 01:39:30 2019 No.11104412 >>11104406We are not google or wikipedia.  >> Anonymous Wed Oct 30 02:06:27 2019 No.11104465 >>11103057Mathematicians dont love complex numbers. They just love gaussian integers. When you see a irrational complex number you leave. Engineers ftw.  >> Anonymous Wed Oct 30 02:07:39 2019 No.11104468 >>11101100I think the issue here is not the modality of finding 3 separate solutions to a problem. I think the issue is that -1 doesn't exist in nature.  >> Anonymous Wed Oct 30 02:53:21 2019 No.11104544 >>11103534have you actually read the post he was replying to ? it's you who's being an annoying pedant  >> Anonymous Wed Oct 30 03:24:01 2019 No.11104587 >>11102209Yes, actually. There are three possible answers, and >it dependson which exact phasor represents the "-1."If [math]-1=e^{i\pi}$, then the cube root of -8 is $2(e^{i\frac{\pi}{3}})$If $-1=e^{i3\pi}$, then the cube root of -8 is $2(e^{i\pi})$If $-1=e^{i5\pi}$, then the cube root of -8 is $2(e^{i\frac{5\pi}{3}})$This is basic fucking arithmetic, and you should be ashamed to accept something as vague and arbitrary as principle roots.
 >> Anonymous Wed Oct 30 03:28:09 2019 No.11104594 >>11101375So what's wrong with this image?
 >> Anonymous Wed Oct 30 03:41:06 2019 No.11104612 >>11101375hm... what job in maths pays 300k?
 >> Anonymous Wed Oct 30 03:43:36 2019 No.11104616 >>11104612in Zimbabwe an apple costs 300k
 >> Anonymous Wed Oct 30 03:45:15 2019 No.11104617 >>11104616they could afford it, they literally have diamonds and gold just lying around everywhere on top of the ground
 >> Anonymous Wed Oct 30 03:45:25 2019 No.11104618   >>11102231yeah it's literally how fucking from language to technologyit's all made up shitit's the fucking applications that matter
 >> Anonymous Wed Oct 30 03:47:11 2019 No.11104620 >>11102231yeah it's literally how everything from language to technology worksit's all made up it's the fucking applications that matter
 >> Anonymous Wed Oct 30 05:13:23 2019 No.11104714 >>11101792What's above sedenions?
 >> Anonymous Wed Oct 30 05:19:03 2019 No.11104722 >>11101083naming it imaginary should've nullified the recognition for conceptualizing it. There's nothing imaginary about it.people invented 0 as well
 >> Anonymous Wed Oct 30 08:20:42 2019 No.11104967 >>11104714>>>google.com>>>wikipedia.com
 >> Anonymous Wed Oct 30 08:47:45 2019 No.11105025 >>11104594you need to use the norms to recover Pythagoras. They did not
 >> Anonymous Wed Oct 30 10:25:34 2019 No.11105229 >cant solve an equation>just make up random numbers that solve it>wow im such a geniusmath is a liberal art
 >> Anonymous Wed Oct 30 10:32:43 2019 No.11105248 >>11105229>math is a liberal artSo you've to be liberal to be good at math ?I'm ok with that.
 >> Anonymous Wed Oct 30 10:33:12 2019 No.11105254 >>11105229So when faced with a problem you just give up?
 >> Anonymous Wed Oct 30 10:34:16 2019 No.11105259 this is the only i I need to know about:for (int i = 0; i < 10; i-=-1) {System.out.println("Math is for faggots");}
 >> Anonymous Wed Oct 30 10:36:00 2019 No.11105261 >java lol
 >> Anonymous Wed Oct 30 10:38:02 2019 No.11105266 >>11105254I turn to God
 >> Anonymous Wed Oct 30 10:41:34 2019 No.11105276 >>11105266checked and blessed>>11105254If you just invent random shit because you can't figure out a problem, and that invention (which you call IMAGINARY for Christ's sake) miraculously has the properties needed to solve the equation, then that's just laziness.
 >> Anonymous Wed Oct 30 10:41:52 2019 No.11105278 File: 58 KB, 650x520, pyth.png [View same] [iqdb] [saucenao] [google] [report] >>11101375>Hypothenuse = i2 + 1 = 0I'm [e^(i.Pi) - 1]K with that.
 >> Anonymous Wed Oct 30 10:52:30 2019 No.11105310 >>11102865lmao this should become a new pasta, using the angry guys speech.
 >> Anonymous Wed Oct 30 10:53:29 2019 No.11105311 >>11105276So what, we throw out all of the theory of DE's, etc. just because you don't like the name? Grow up. The math works. Maybe come back after taking a course in analysis and realize how fucking stupid you sound.
 >> Anonymous Wed Oct 30 10:55:05 2019 No.11105320 >>11105311>analyzing the dreams and lsd trips of 1600s mathemagicians. No thanks. My time is far too valuable.
 >> Anonymous Wed Oct 30 10:55:26 2019 No.11105323 >>11104620Fourier transforms
 >> Anonymous Wed Oct 30 10:56:33 2019 No.11105326 >>11105320>My time is far too valuable.>spends embarrassing himself on /sci/uh huh
 >> Anonymous Wed Oct 30 10:57:28 2019 No.11105328 >>11105320you've done nothing with it up to now
 >> Anonymous Wed Oct 30 10:57:49 2019 No.11105329 Mathematics isn't invented you stupid fucking morons.That the imaginary numbers close the Reals is an intrinsic and beautiful aspect of reality. No one "made this up" the Italian realized that this works and wrote a paper on it. Just like no one "made up" zero or negative numbers or any other mathematical idea.
 >> Anonymous Wed Oct 30 10:58:29 2019 No.11105332 >>11105276>If you just invent random shit because you can't figure out a problem, and that invention (which you call IMAGINARY for Christ's sake) miraculously has the properties needed to solve the equation, then that's just laziness.imagine that some people unironically believe this
 >> Anonymous Wed Oct 30 10:58:38 2019 No.11105334 >>11105329>Mathematics isn't inventedyes it is
 >> Anonymous Wed Oct 30 11:01:13 2019 No.11105343 >>11104587nigga learn something about covering spaces
 >> Anonymous Wed Oct 30 11:02:17 2019 No.11105345 >>11105334No it isn't Whatever tautologies you find from a set of WFF is intrinsic to the set and isn't invented, you can only discover them.You can not invent Euclidian geometry, once you have the axioms the set of true statements are always true and uninvented.
 >> Anonymous Wed Oct 30 11:02:46 2019 No.11105349 File: 9 KB, 225x225, cringejak.png [View same] [iqdb] [saucenao] [google] [report] >people still arguing about imaginary numbers>Nobody arguing about the powerset axiom
 >> Anonymous Wed Oct 30 11:05:30 2019 No.11105354 >>11105345you always invent the axioms though
 >> Anonymous Wed Oct 30 11:10:23 2019 No.11105364 >>11105354You, you discover axioms a posteriori using your senses, mathematics is both empirical and rational.The foundations of mathematics are in a posteriori counting, which is not invented. The axioms built on top of that are not invented either, they are discovered based on the observations of how counting works. Then LITERALLY ALL OF MATHEMATICS THAT WE USE NOW are rationalized from the set of WFF that we built off of the discovery of counting.All of math is discovered, none of it is invented. Imaginary numebrs are not invented, made up, or imaginary. They are real, there exists a number that you square and get negative one, and in fact it forms an algebraically closed field over the reals that is unique up to isomorophism.None of this shit is invented and I'm tired of engineer fucking retards saying it is. When a mathematician writes a new theorem of all those crazy symbols he is discovering a new intrinsic aspect of reality no matter how abstract it is.
 >> Anonymous Wed Oct 30 11:10:58 2019 No.11105366 >>11105349do you honestly think most people on /sci/ have taken a course in set theory?
 >> Anonymous Wed Oct 30 11:14:34 2019 No.11105377 >>11105345>Whatever tautologies you find from a set of WFF is intrinsic to the set and isn't inventedMaths are based on the cultures it evolved from.>You can not invent Euclidian geometryYou can imagine a world where those E.T. Mathematicians :- Have no fingers : So no base 10 or 12 or 20 or whatever.- They live in water : No 2D plan, then no Euclydian in a plan, but perhaps 3D mat based on volumetry.- Another one if they live in water : Base 2 could be a math model, "closed palm" = 1 and "opened palm" = 0.- Etc.
 >> Anonymous Wed Oct 30 11:15:59 2019 No.11105385 >>11105364fundamental theorem of calculus is a discovery, but riemann integral is an invention
 >> Anonymous Wed Oct 30 11:25:15 2019 No.11105408 >>11101375literally rekt lmao
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