Answer
{$-8i,8i$}
Work Step by Step
We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain:
Step 1: $(x)^{2}=-64$
Step 2: $x=\pm \sqrt {-64}$
Step 3: $x=\pm \sqrt {-1\times64}$
Step 4: $x=\pm \sqrt {-1}\times\sqrt {64}$
Step 5: $x=\pm (i\times\sqrt {64})$ [as $i=\sqrt {-1}$]
Step 6: $x=\pm (i\times8)$
Step 7: $x=\pm (8i)$
Step 8: $x=8i$ or $x=-8i$
Therefore, the solution set is {$-8i,8i$}.
