# Complex root

I just bombed a quiz because it was 2 questions and this was one of them:

Find all three complex roots of the following equation (give answers in polar and rectangular form)

$$z^3+8=0$$

Looks easy enough,

$$z=2e^{-i\frac{\theta}{3}}$$

This is where I think I completely realized I wasn't sure what I was doing. My roommate suggested I look for the roots of unity which I know that:

$$r^n(cos(n\theta)+isin(n\theta))=1+i*0$$

so if I want to consider mine it should be:

$$8^{1/3}(cos(\frac{\theta}{3})+isin(\frac{\theta}{3})=-8$$

so then

$$\theta=\frac{k2\pi}{3}$$

is this the right track?

Last edited: