How to write in polar form

Question

To write in polar form you use this formula $$z=a+bi=r \left(\cos \theta+i\sin\theta \right)$$ I want the polarform for this rectangular function$$4\sqrt2(-1+i)$$

See this for more information Complex number from a region

Answer 1

HINT: the polar form of $a+ib$ is $|a+ib| e^{\rm{Arg}(a+ib)}$.

Answer 2

If I understood problem correctly, then $$ -1+i = \sqrt{1+1} \left\{ \cos \left[ \text{atan2}(1,-1)\right] + i\sin \left[ \text{atan2}(1,-1)\right]\right\} $$ where you can find info about $\text{atan2}(y,x)$ here. So $\theta = -\frac \pi 4 + \pi = \frac {3\pi}4$.

And finally $$ 4 \sqrt 2(-1+i) = 8 \left( \cos \frac {3\pi}4 + i \sin \frac {3\pi}4\right) $$