/sci/ - Science & Math

[Pedro No.5858540]

>e^(i*i)=cos(i)+i*sin(i)
>sin(i)=i*sinh(1)=i*1.1752...
>i*sin(i)=i*i*1.1752...=-1.1752...
>i*sin(i)=-1.1752...
>cos(i)=cosh(1)=1.5430...
>e^(i*i)=-1.1752...+1.5430...=1.5430...-1.1752...
>e^(i*i)=0.3678...

>mfw

>e^(i*i)=e^(-1)=0.3678...

[Anonymous No.5858559]

>>5858540

and how do you explain step 1?

[Anonymous No.5858565]

>>5858559
e^(i*x)=isin(x)+cos(x)

[Anonymous No.5858596]

What is your point?

[Anonymous No.5858601]

>>5858596

That if you write out two provably equivalent statements and calculate their values you'll find that they're equal?

I dunno, he's got me, too.

[Anonymous No.5858656]

You know you could just write i*i as -1 and skip all the bullshit with hyperbolics.

[Anonymous No.5858664]

Guys did you know that <span class="math"> (\sqrt{2})(\sqrt{2}) = 2.[/spoiler]

[Anonymous No.5858665]

>>5858540

[Anonymous No.5858678]

>>5858664
wonder what happens if you calculate the left hand side and the right hand side?

[Anonymous No.5858692]

>>5858665
The difference here is that the identity of i^i is actually kind of cool.

e^(i*i) is just obvious though.

[Anonymous No.5858699]

>>5858678
<span class="math">(\sqrt{2})(\sqrt{2}) = 2[/spoiler]
<span class="math">\implies (1.41421356237)(1.41421356237) = 2[/spoiler]
<span class="math">\implies 2 = 2[/spoiler]

[Anonymous No.5858698]

>>5858692
No, i^i has no unique value, it has infinitely many values. It's not interesting in the mildest.

What's so cool about this is that it's a nice example that e^(i*x)=cos(x)+i*sin(x) is consistent with the rest of math.

[Anonymous No.5858710]

>>5858699
What?
<span class="math">\implies[/spoiler]
<span class="math">\rightarrow[/spoiler]
<span class="math">\to[/spoiler]

[Anonymous No.5859039]

>>5858540
also
cosh(1) + sinh(1) = e
cosh(1) - sinh(1) = 1/e