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  4. A point ' z ' moves on the curve | z -4-3 i |=2 in an argand plane. The maximum and minimum values of | z | are -

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Q. A point ' $z$ ' moves on the curve $| z -4-3 i |=2$ in an argand plane. The maximum and minimum values of $| z |$ are -

Complex Numbers and Quadratic Equations

Solution:

image
$|z-4-3 i|=2$ represents a circle with centre $(4,3)$ and radius 2.
so minimum and maximum distances from origin will be
$OP - r$ and $OP + r$ respectively.
$|z|_{\min }=5-2=3 $
$|z|_{\max }=5+2=7$