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

Question

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

Beauty is in the $\pm i$ of the beholder. – robjohn Oct 29 '14 at 00:49 — robjohn, Oct 29 '14 at 00:49
that was really creative thing to say. – Firas Abd El Gani Oct 29 '14 at 00:51 — Firas Abd El Gani, Oct 29 '14 at 00:51

score 5 · Accepted Answer · answered Oct 29 '14 at 00:11

5

We have

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

answered Oct 29 '14 at 00:11

1 Answers1