Finding Values of Complex Equation

[ver_mathstats]

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!

 

[anuttarasammyak]

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 ?