Solve by Factoring z^2+8=4

$z^{2} + 8 = 4$

Step 1

Subtract $4$ from both sides of the equation.

$z^{2} + 8 - 4 = 0$

Step 2

Subtract $4$ from $8$ .

$z^{2} + 4 = 0$

Step 3

Subtract $4$ from both sides of the equation.

$z^{2} = - 4$

Step 4

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

$z = \pm \sqrt{- 4}$

Step 5

Simplify $\pm \sqrt{- 4}$ .

Rewrite $- 4$ as $- 1 (4)$ .

$z = \pm \sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$z = \pm \sqrt{- 1} \cdot \sqrt{4}$

Rewrite $\sqrt{- 1}$ as $i$ .

$z = \pm i \cdot \sqrt{4}$

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

$z = \pm i \cdot \sqrt{2^{2}}$

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

$z = \pm i \cdot 2$

Move $2$ to the left of $i$ .

$z = \pm 2 i$

Step 6

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.

$z = 2 i, - 2 i$