Solve for z z^6=-64

$z^{6} = - 64$

Step 1

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

$z = \pm \sqrt[6]{- 64}$

Step 2

Simplify $\pm \sqrt[6]{- 64}$ .

Rewrite $- 64$ as ${(2 i)}^{6}$ .

$z = \pm \sqrt[6]{{(2 i)}^{6}}$

Pull terms out from under the radical, assuming positive real numbers.

$z = \pm 2 i$

Step 3

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.

$z = 2 i$

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

$z = - 2 i$

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

$z = 2 i, - 2 i$