Not certain about Complex Number, Polar Form Question

[linuxux]

Homework Statement

The question:
a)Solve the equation $$z^{3}=4\sqrt{2}-4\sqrt{2}i.$$.
b)Express the answer in polar form.

The Attempt at a Solution

Here's what i got:

$$r=\sqrt{\left(4\sqrt{2}\right)^{2}+\left(-4\sqrt{2}\right)^{2}}=8$$
$$\tan^{-1}\left(\frac{-4\sqrt{2}}{4\sqrt{2}}\right)=-45^{o}$$
$$z^{3}=8^{3}cis\left(-45\cdot3\right)$$
$$z^{3}=512\left(cos\frac{5\pi}{4}-i\sin\frac{5\pi}{4}\right)$$
$$z^{3}=512\left(\frac{-\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i\right)$$
$$=-256\sqrt{2}+256\sqrt{2}i\right)$$

im not sure if this is right, I am supposed to graph this, and with these kinds of numbers, i figure i went wrong somewhere, i have no idea what they mean by "solve" and how or if this "solves" anything other than the fact that it ends with an equal sign, so if someone can check it for me id appreciate it, thanks."

 

[mjsd]

i think you are solving for z, so you should have
$$z^{3}=4\sqrt{2}-4\sqrt{2}i=8 cis\left(-45\right)$$
and then cube root both sides...
hint: should get 3 roots

 

[linuxux]

oh, so i went too far, now i see what I am supposed to be solving, thanks.