Question

Let z=2-5i
a)Write z in polar form.
b) Find the complex number z^3 and express it in polar form.
c) Find the three cube roots of z and express them in polar form.

Answer 1

When \(z=a+bi\),
\[r=\sqrt{a^2+b^2}\]and\[\theta_r=tan\frac{b}{a}\]But let's draw it!We know it's in the lower-right quadrant, so our \(\theta\) will be given by \(2\pi - \theta_r\).

Finally, what does the final form look like?
\[z=r(cos\theta + isin\theta)\]