Question

What are the fourth roots of −4 + 4√4i

Answer 1

Answer:

Explanation:

Given:

$-4+4\sqrt{4i}$

To find:

The fourth roots

Let's first find the square roots of −4 + 4√4i as seen below;

$\begin{gathered} =\pm\sqrt{-4+4\sqrt{4i}} \\ =\pm\sqrt{-4+4\sqrt{4*i}} \\ =\pm\sqrt{-4+8\sqrt{i}} \\ =\pm\sqrt{4(-1+2\sqrt{i}} \\ =\pm2\sqrt{-1+2\sqrt{i}} \end{gathered}$