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  4. The minimum value of |z| , if |.z-2-2i|.=1 , is

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

NTA AbhyasNTA Abhyas 2020Complex Numbers and Quadratic Equations

Solution:

$\left|\right.z-\left(\right.2+2i\left.\right)\left|\right.=1$ represents a circle
of radius $1$ and centre $C\left(\right.2+2i\left.\right)$ .
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 $=2\sqrt{2}-1$