Chapter 12, Problem 1CR

To determine

To calculate: The real and complex solutions of the equation $\left|x^2\right|=9$.

Answer to Problem 1CR

Solution:

The real and complex solutions of the equation $\left|x^2\right|=9$ are $x=\pm 3$ or $x=\pm 3i$.

Explanation of Solution

Given information:

The equation, $\left|x^2\right|=9$

Formula used:

If $\left|x\right|=a$ then $x=a$ or $x=-a$.

Calculation:

Since the given equation contains absolute value of $x^2$ it can be rewritten as,

$x^2=9$ or $x^2=-9$

Taking square root on both sides,

$\Rightarrow x=\pm \sqrt{9}$ or $x=\pm \sqrt{-9}$

$\Rightarrow x=\pm 3$ or $x=\pm 3i$

Hence, the solutions of equation $\left|x^2\right|=9$ are $x=\pm 3$ or $x=\pm 3i$.