Question

Find the real and complex solution of the equation $x^2=-12$.

Short answer

The complex solutions are $x=-i2\sqrt{3},i2\sqrt{3}$.

Step-by-step solution

Step 1. Solve for the given quadratic.

$\begin{array}{c}{x}^2=-\mathrm{12....}\left(\text{Given}\right)\\ \text{or,}x=\pm \sqrt{-12}\end{array}$

Step 2. By concept of complex numbers.

Solve for $x=\pm \sqrt{-12}$further,

$\begin{array}{c}x=\pm \sqrt{-12}\\ \text{or,}x=\pm \sqrt{\left(12\right)\left(-1\right)}\\ \text{or,}x=\pm i2\sqrt{3}\mathrm{....}\left(\sqrt{-1}=i\right)\\ x=-i2\sqrt{3},i2\sqrt{3}\end{array}$

Step 3. DESCRIPTION OF STEPS.

Since the roots are complex hence it has complex solution $x=-i2\sqrt{3},i2\sqrt{3}$.