Question

The minimum value of $\left|z\right|$ , if $|z-2-2i|=1$ , is

• A. $2\sqrt{2}-1$
• B. $2\sqrt{2}$
• C. $2\sqrt{2}+1$
• D. $2\sqrt{2}-2$

Answer 1

Answer: (A)

$|z-(2+2i)|=1$ represents a circle
of radius $1$ and centre $C(2+2i)$ .
Minimum value of $OP$ (where, $P$ is any point on the circle and $O$ is the origin) i.e
Minimum value of $\left|z\right|=OC-$ radius $=2\sqrt{2}-1$