Appendix A - Review - A.7 Complex Numbers; Quadratic Equations in the Complex Number System - A.7 Assess Your Understanding - Page A61: 55

$\{-2i,2i\}$

Subtract $4$ from both sides. $x^2+4-4=0-4$ Simplify. $x^2=-4$ Use square root property. $x=\pm \sqrt{-4}$ $x=\pm \sqrt{4(-1)}$ $x=\pm \sqrt{4}\cdot \sqrt{-1}$ Use $\sqrt{4}=2$ and $\sqrt{-1}=i$. $x=\pm 2i$ Hence, the solution set is $\{-2i,2i\}$.