/sci/ - Science & Math

What is e^(-ti) in rectangular form? I cannot tell if I am genuinely retarded but I searched on Google for like 30 mins (albeit not all in one session) and I couldn't find the answer to this simple question. I know e^(ti) is cos(t)+sin(t)i but what happens when the phasor is negative?

If I were to travel away from you at the speed of light, I would look completely still to you because in order to see me, you need to see the light reflected off of me but that light will take longer and longer to reach you as I approach the speed of light. I can thus understand why time slows down for an object relative to another object as they move away from eachother. There are two things that I cannot conceptually grasp about relativity, however.
1) Why is time travel possible with this analogy in mind? In the analogy, to both individuals, time is moving normally for themselves. If I were to reverse direction and head back home, why would you have aged more? Or wait, would I have aged more? Using this basic analogy, it seems as though the only reason as to why I seem to not be aging is because you are essentially watching a frozen afterimage of because of how fast I am moving away from you. My actual age has no relevance to what you are seeing. I'm guessing that I'm not understanding a crucial concept behind how space and time are woven together.
2)Why does simply being under the influence of higher gravity make you age less relative to someone at lower gravity? Here's what I do understand: gravity is the result of curved space from massive objects. What I don't understand: how exactly does space get curved and why does the more warped space gets (more massive/gravity) the longer light takes to travel?

My small brain cant fathom this all

I've finished E&M and just recently completely acoustics/optics. What other fields of physics do I have left to study before I tackle modern stuff?

>>9715995
thank you for the protocol, smartass

>>9695551
>be mathfag
>intellectually incapable to understand the quick sort-like algorithm to compute the median so you call it "the silly tournament game" instead
>not knowing one of the most trivial numerical methods
>not knowing quick sort
Mathfags are mega brainlets. CS majors win again.

What do gradients exactly represent? Ok, so here's the part that confuses me. The first derivative is supposed to be the tangent right? Apparently the first order gradient is a vector normal to the surface. When exactly is the vector normal or tangent or neither. This shit is confusing me.

>wut if i put pic sidwei

IQ means nothing anyway.

>>9545830
>Australia
>continent

>atoms are inobservable they said
>anon, you're stupid and don't deserve a scientific education they said

>real analysis harder than Stokes' theorem

>equal and opposite reaction
>renewable energy
>tiny variation of [math]x[/math]
>[math]\mathbf\nabla\ =\ \begin{pmatrix} \frac\partial{\partial x} \\ \frac\partial{\partial y} \\ \frac\partial{\partial z} \end{pmatrix}[/math]
>[math]\sin\ x\ \approx\ x[/math]
>[math]n!\ \approx\ \mathrm e^n[/math]
>[math]\mathscr P\left(x\right)[/math] for some [math]x[/math]
>the function [math]f\left(x\right)[/math]
>inverse square law
>[math]\left\{\right\}[/math]
>[math]a_1\ +\ a_2\ +\ \cdots\ +\ a_n[/math]
>[math]\sin^2\ x\ =\ \left(\sin\ x\right)^2[/math], but [math]\sin^{-1}\ x\ =\ \arccos\ x[/math]
>"calculus" and "real analysis" as 2 different courses
>assume a flat, frictionless and infinite surface
>it's in multiple places at the same time
>the uncertainty principle
>degrees Kelvin
>the Dirac delta function
>entropy is disorder
>voltage is the electric field
>the Earth revolves around the Sun
>this series doesn't converge, let's regularize it

>>9475339
>too lazy to schedule computer task
>"i hurvv lif awwtserd ev werrk"