Precalculus Examples

$x^{3} + 8 i = 0$

Step 1

Subtract $8 i$ from both sides of the equation.

$x^{3} = - 8 i$

Step 2

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

$x = \sqrt[3]{- 8 i}$

Step 3

Simplify $\sqrt[3]{- 8 i}$ .

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Step 3.1

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$x = \sqrt[3]{{(- 2)}^{3} i}$

Step 3.2

Pull terms out from under the radical.

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

Step 4