Question

Math proof help.
Prove i ^(4k + n) = i^n , k as an element of the set Z

Answer 1

What re we proving exactly?
Am i missing smth or is this the complete question?

Answer 2

Its to prove:
\[i ^(4k +n) = i^n\]

Answer 3

So i think we take the limit of k or n approaching infinity? or maybe a series?

Answer 4

what identity is that?

Answer 5

Does this work\[i=e^{i\pi/2} \implies i^{4k} = e^{i2\pi k}=1\]

Answer 6

I think so yes

Answer 7

I should be able to split the 4k and n leaving just the resultant

Answer 8

What identity is that? i see it relates to euler but not quite the same

Answer 9

famuliar wid euler's formula right \[e^{i\theta}=\cos(\theta)+i\sin(\theta)\]

Answer 10

plugin \(\theta=\pi/2\), we get
\[e^{i\pi/2}=\cos(\pi/2)+i\sin(\pi/2)=0+i*1=i\]

Answer 11

plugin \(\theta=2\pi k\), we get
\[e^{i2\pi k}=\cos(2\pi k)+i\sin(2\pi k)=1+i*0=1\]

Answer 12

http://mathworld.wolfram.com/EulerFormula.html