Please help asap!

I answerd that, but why doesn't it count as me. I just registered

Suppose z  is a complex number such that $z^3 = 100+75i$ . Find |z|

$|z^3| = \sqrt{100^2+75^2}\\ |z^3| = \sqrt{100^2+75^2}\\ |z^3| = 125\\ z^3=125[\frac{100+75i}{125}]\\ z^3=125[\ 0.8+0.5i]\\ $

Let

$z=re^{i\theta}\\ z^3=r^3e^{3i\theta}\\ z^3=r^3(cos(3\theta) +isin(3\theta))\\ $
$r^3(cos(3\theta) +isin(3\theta))=125[\  0.8+0.6i]\\ r^3=125\\ r=5\\ cos(3\theta)=0.8\\ sin(3\theta)=0.6\\ 3\theta \approx 0.6435\\ \theta \approx 0.2145\;radians\\ $

anyway, I digress,

$|z|=5$