Find All Complex Solutions z^4=-1

$z^{4} = - 1$

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

$z = \pm \sqrt[4]{- 1}$

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.

$z = \sqrt[4]{- 1}$

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

$z = - \sqrt[4]{- 1}$

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

$z = \sqrt[4]{- 1}, - \sqrt[4]{- 1}$