Question

Find all the solutions, real and complex, of the equation$\left|x^2\right|=9$

Short answer

The solution is $x=-3,3,-3i,3i$.

Two roots are real and two are imaginary.

Step-by-step solution

Step 1. Given Information

Given equation is$\left|x^2\right|=9$

Step 2. Finding solution

$$\begin{gathered} \left|x^2\right|=9 \\ {x}^2=\pm 9 \\ {x}^2=9or{x}^2=-9 \end{gathered}$$

Now,$$\begin{gathered} x^2=9 \\ x=\pm 3 \\ and \\ {x}^2=-9 \\ x=-3i,3i \end{gathered}$$