[Math] Find all complex numbers $z$ satisfying the equation

Question

I need some help on this question. How do I approach this question?

Find all complex numbers $z$ satisfying the equation

$$
(2z – 1)^4 = -16.
$$

Should I remove the power of $4$ of $(2z-1)$ and also do the same for $-16$?

Answer 1

HINT: How many solutions does $x^4+16=0$ have?

$x_{1,2,3,4}= \sqrt{2}(\pm 1 \pm i)$, substitute $x$ with $2z-1$, solve for $z$ and you're done.