Question

If $|z-\frac{4}{z}|$ =2, then the maximum value of $\left|z\right|$ is

• A. +1
• B. +1
• C. -1
• D. -1

Answer 1

The correct option is B

+1

$\left|z\right|$ = $|z-\frac{4}{z}+\frac{4}{z}|$
$\le$ $|z-\frac{4}{z}|$+ $\left|\frac{4}{z}\right|$
= $|z-\frac{4}{z}|$ + $\frac{4}{\left|z\right|}$
$\left|z\right|$ $\le$ 2 + $\frac{4}{\left|z\right|}$
${\left|z\right|}^2$ - 2$\left|z\right|$ $\le$ 4
${\left|z\right|}^2$- 2$\left|z\right|$ +1 $\le$ 5
$\Rightarrow$ $\left|z\right|$ $\le$ $\sqrt{5}$ +1