Finite Math Examples

$| z + 3 i | = 4$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$z + 3 i = \pm 4$

Step 2

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

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$z + 3 i = 4$

Step 2.2

Subtract $3 i$ from both sides of the equation.

$z = 4 - 3 i$

Step 2.3

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

$z + 3 i = - 4$

Step 2.4

Subtract $3 i$ from both sides of the equation.

$z = - 4 - 3 i$

Step 2.5

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

$z = 4 - 3 i, - 4 - 3 i$