How do I solve $x^4+44=0$ according to de Moivre?

Question

How do I solve $x^4+44=0$ according to de Moivre?

I tried to use the formula, but I got roots that are not beautiful numbers. What should the complex roots for this equation be?

Answer 1

We have

$$x^4=-44=44 e^{i\pi}\implies x=\sqrt[4]{44}\exp\left(\frac{i\pi}4+\frac{ik\pi}2\right),\; k=0,1,2,3 $$