Question

If $|z-2+i|\le 2$, then find the greatest and least value of $|z|$.

Answer 1

$|z-2+i|=2$

$\therefore z-2+i=\pm 2$

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$z-2+i=2$

$z=2+2-i=4-i\Rightarrow |z|=\sqrt{4^2+(-1{)}^2}=\sqrt{17}$

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$z-2+i=-2$

$z=-2+2-i=-i\Rightarrow |z|=\sqrt{0^2+(-1{)}^2}=1$

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Greatest value of $|z|=\sqrt{17}$

Least value of $|z|=1$