Determine all the roots of the equation given by $z^2(1-z^2)=16.$

Question

For my third year Complex variable course, the question is

Determine all the roots of the equation given by $$z^2(1-z^2)=16.$$

My attempt: Let $z^2 = x$
$x(1-x) = 16$
$x-x^2 = 16$
$x^2-x-16 = 0$
$x = \frac{1 \pm \sqrt{1 -4(16)}}{2}$
$x = \frac{1 \pm \sqrt{-63}}{2}$
$x = \frac{1 \pm i\sqrt{63}}{2}$
$z^2 = \frac{1 \pm i\sqrt{63}}{2}$

Am I correct so far?

BTW the question is worth $5$ marks.

Answer 1

Remember it is a fourth order equation, so the complete solution has four roots, in this example they occur in complex-conjugate pairs.