Q:

Problems solving a Complex exponential equation

The equation is: $z^3=1+i$
I am supposed to use this formula. 
Length= $^n\sqrt(R)$
And the rotation is given by $\theta/n$
n is the exponential number. And $+p\cdot2pi/n$ represents all the other solutions.
By using this i should have found the answer and it worked in other cases when z³=i
However in this assignment...
R is the modulos or the length. When i take the lenght of (1+i) i get $\sqrt2$ and because of that sqaure root i suspect i did something wrong.I hope someone can explain my mistake, and give me a tip to do it right. 

A:

If we write $z=re^{i\theta}$, then $$z^3=r^3e^{3i\theta}=1+i=\sqrt2e^{\pi i/4}$$ Taking cube roots gives$$z=\sqrt[6]2e^{\pi i/12}$$  Of course, we can multiply by a cube root of $1$ to get two other answers, so the full solution is $$z\in\{\sqrt[6]2e^{\pi i/12},\sqrt[6]2e^{9\pi i/12},\sqrt[6]2e^{17\pi i/12}\}$$

