Question involving De Moivre's Theorem Hey guys,

I've been stuck on this question 1b in the image. I got 1a...writing it in general polar form but I'm really not sure of the procedure used to do 1b.

Could someone please give some step-by-step instructions to how I can get solve it?

Any help would be much appreciated. 

Thanks!
Well, you need to convert the terms to polar form to adequately use De Moivre's Theorem.

$$ z^2 = i - 1  = \sqrt{2}e^{i(3\pi/4)}$$

You should be able to use De Moivre's Theorem from here.
a) $r = \sqrt {1^2 + 1^2} = \sqrt{2}$ and $\theta = \tan^{-1}⁡\left(\frac {-1}{1} \right) =  \frac {3 \pi}{4}$

Therefore $w = \sqrt{2}~ \mathrm{cis} \left(\frac{3\pi}{4}+ 2k\pi\right)$

b) $$\begin{align} z + 1 - i = 0 \implies z &amp;= -1 + i \\ &amp;= \left (\sqrt{2} ~ \mathrm{cis} \left( \frac{3 \pi}{4} + 2k \pi \right)\right)^2 \\ &amp;= 2~  \mathrm{cis}^2~ \left(\frac{3\pi}{4} + 2k\pi\right) \\ &amp;= 2 ~ \mathrm{cis} \left(\frac{3 \pi}{2} + 4k\pi\right) \end{align}$$