Precalculus Examples

$| a - i | = \sqrt{37}$

Step 1

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

$a - i = \pm \sqrt{37}$

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.

$a - i = \sqrt{37}$

Step 2.2

Add $i$ to both sides of the equation.

$a = \sqrt{37} + i$

Step 2.3

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

$a - i = - \sqrt{37}$

Step 2.4

Add $i$ to both sides of the equation.

$a = - \sqrt{37} + i$

Step 2.5

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

$a = \sqrt{37} + i, - \sqrt{37} + i$