Question

If $z$ is a nonzero complex number then$\left|\frac{|\overline{z}{|}^2}{z\overline{z}}\right|$is equal to

• A. $\left|\frac{\overline{z}}{z}\right|$
• B. $1$
• C. $|\overline{z}|$
• D. none of these

Answer 1

Answer: (A), (B)

The correct options are
A $\left|\frac{\overline{z}}{z}\right|$
B $1$

$w=\left|\frac{{\left|\overline{z}\right|}^2}{z\overline{z}}\right|$
$\Rightarrow w=\frac{\left|\overline{z}\right|\left|\overline{z}\right|}{\left|z\right|\left|\overline{z}\right|}=\frac{\left|\overline{z}\right|}{\left|z\right|}$
$\therefore w=\left|\frac{\overline{z}}{z}\right|$
$\Rightarrow w=\frac{\left|\overline{z}\right|}{\left|\overline{z}\right|}$ ...{ $\because \left|z\right|=\left|\overline{z}\right|$}

$\therefore w=1$
Hence, options 'A' and 'B' are correct.