Finding Values of Complex Equation

ver_mathstats
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Homework Statement
Find the values of ((1-i)/sqrt(2)) ^ (i+1)
Relevant Equations
((1-i)/sqrt(2)) ^ (i+1)
I took the equation and rewrote it as: e(i+1)(log(1-i)-log(√2)).

So I worked on it in sections meaning e(i+1) and then log(1-i).

For e(i+1) I got eie1 and used Euler's formula for ei to get: e1(cos(1)+isin(1)).

And then for log(1-i) I got ln√2 + i(-(π/4)+2kπ).

Do I just bring them together now? Or would I first FOIL the exponent at the very beginning as in this part "(i+1)(log(1-i)-log(√2))"? Any help would be appreciated thank you!
 
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ver_mathstats said:
Relevant Equations:: ((1-i)/sqrt(2)) ^ (i+1)

I took the equation and rewrote it as: e(i+1)(log(1-i)-log(√2)).

So I worked on it in sections meaning e(i+1) and then log(1-i).
I take it
[e^{-\frac{\pi i}{4}}]^1 [e^{-\frac{\pi i}{4}}]^i
Does this work ?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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