Find All Complex Solutions x^4=-2+2 square root of 3i

$x^{4} = - 2 + 2 \sqrt{3} i$

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{- 2 + 2 \sqrt{3} i}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt[4]{- 2 + 2 \sqrt{3} i}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt[4]{- 2 + 2 \sqrt{3} i}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt[4]{- 2 + 2 \sqrt{3} i}, - \sqrt[4]{- 2 + 2 \sqrt{3} i}$