Find All Complex Solutions x^4=-16

$x^{4} = - 16$

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

$x = \pm \sqrt[4]{- 16}$

Simplify $\pm \sqrt[4]{- 16}$ .

Rewrite $- 16$ as $2^{4} \cdot - 1$ .

Factor $16$ out of $- 16$ .

$x = \pm \sqrt[4]{16 (- 1)}$

Rewrite $16$ as $2^{4}$ .

$x = \pm \sqrt[4]{2^{4} \cdot - 1}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt[4]{- 1}$

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.

$x = 2 \sqrt[4]{- 1}$

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

$x = - 2 \sqrt[4]{- 1}$

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

$x = 2 \sqrt[4]{- 1}, - 2 \sqrt[4]{- 1}$