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## Homework Statement

The question:

**a)Solve the equation [tex]z^{3}=4\sqrt{2}-4\sqrt{2}i.[/tex].**

b)Express the answer in polar form.

b)Express the answer in polar form.

## The Attempt at a Solution

Here's what i got:

[tex]r=\sqrt{\left(4\sqrt{2}\right)^{2}+\left(-4\sqrt{2}\right)^{2}}=8[/tex]

[tex]\tan^{-1}\left(\frac{-4\sqrt{2}}{4\sqrt{2}}\right)=-45^{o}[/tex]

[tex]z^{3}=8^{3}cis\left(-45\cdot3\right)[/tex]

[tex]z^{3}=512\left(cos\frac{5\pi}{4}-i\sin\frac{5\pi}{4}\right)[/tex]

[tex]z^{3}=512\left(\frac{-\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i\right)[/tex]

[tex]=-256\sqrt{2}+256\sqrt{2}i\right)[/tex]

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."

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