# Chapter 9 - Section 9.4 - Imaginary Numbers as Solutions of Quadratic Equations - Exercise Set: 23

$y=\left\{ -3-3i\sqrt{2},-3+3i\sqrt{2} \right\}$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property) and using $i=\sqrt{-1}$, the solutions to the given equation, $(y+3)^2=-18 ,$ are \begin{array}{l}\require{cancel} y+3=\pm\sqrt{-18} \\\\ y+3=\pm\sqrt{-1}\cdot\sqrt{18} \\\\ y+3=\pm i\cdot\sqrt{9\cdot2} \\\\ y+3=\pm i\cdot\sqrt{(3)^2\cdot2} \\\\ y+3=\pm i\cdot3\sqrt{2} \\\\ y+3=\pm 3i\sqrt{2} \\\\ y=-3\pm 3i\sqrt{2} .\end{array} Hence, $y=\left\{ -3-3i\sqrt{2},-3+3i\sqrt{2} \right\} .$

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