Question

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

Answer 1

Given that,

$|z-\frac{4}{2}|=2$

$\Rightarrow |z-2|=2$

The above equation indicates a circle

$\Rightarrow z$ is a circle of radius $2$, centred at $(2,0)$

$\Rightarrow z_{max}=4$

$|z{|}_{max}=4$