I need help with this problem

Question

-1

723

4

+202

Suppose that \(z\) is a complex number such that \(z^4 = \frac{64}{5}-\frac{48}{5}i\). Find \(|z|\).

Any help would be greatly appreciated!

Impasta Feb 2, 2020

Melody · Answer 1 · 2020-02-02T09:33:31

I put the answer into Wolfram|Alpha and it says the answer is 2.

I have forgotten how to do it myself though.

Guest · Answer 2 · 2020-02-03T10:59:20

The magnitude of the cn on the RHS is \(\displaystyle \sqrt{\left(\frac{64}{5}\right)^{2}+\left(\frac{48}{5}\right)^{2}}=16, \)

so the magnitude of z is the fourth root of 16, which is 2.