Question

If ${\left|z\right|}^2-3=3\left|z\right|$, then the value of $\left|z\right|$ is

• A. $1$
• B. $\frac{3+\sqrt{21}}{2}$
• C. $\frac{\sqrt{21}-3}{2}$
• D. none of these

Answer 1

The correct option is B $\frac{3+\sqrt{21}}{2}$

$|z{|}^2-3=3|z|$
$|z{|}^2-3|z|-3=0$
$|z|=\frac{3\pm \sqrt{21}}{2}$
$|z|=\frac{3+\sqrt{21}}{2}$