Question

Express z=-1-i in polar form, and then find z^3.

Answer 1

you need two numbers, \(r\) and \(\theta\)
\[r=\sqrt{a^2+b^2}=\sqrt{1+1}=\sqrt{2}\] and \[\theta=\frac{5\pi}{4}\] from the picture

Answer 2

gives
\[\sqrt{2}\left(\cos(\frac{5\pi}{4})+i\sin(\frac{5\pi}{4})\right)\]