Find the Roots (Zeros) x^4+1=0

$x^{4} + 1 = 0$

Subtract $1$ from both sides of the equation.

$x^{4} = - 1$

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

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

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.

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

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

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

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

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