Question

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

Answer 1

Step-by-step explanation:

Given:

`-4+4√(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√(4i)} \\ =\pm\sqrt{-4+4√(4*i)} \\ =\pm\sqrt{-4+8√(i)} \\ =\pm\sqrt{4(-1+2√(i)} \\ =\pm2\sqrt{-1+2√(i)} \end{gathered}`