Question

Use square roots to solve the equation x^2 = -64 over the complex numbers.

Answer 1

$\bf x^2=-64\implies x=\pm\sqrt{-64}\implies x=\pm\sqrt{-1\cdot 64} \\\\\\ x=\pm\sqrt{-1}\cdot \sqrt{64}\implies x=\pm i\cdot 8\implies x=\pm 8i$