Evaluate |a-i| = square root of 37

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

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

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

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.

$a - i = \sqrt{37}$

Add $i$ to both sides of the equation.

$a = \sqrt{37} + i$

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

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

Add $i$ to both sides of the equation.

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

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

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