Let |z-3+2i| $\leq$ 4 , then the absolute different between the maximum and minimum values of |z| is

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Solution

The correct option is C

Let C = 3 - 2i be the centre of the circle |z-3+2i|= 4 . Join the origin to C and let it meet the circle in A and B (see figure) .

Least value of |z| = OB

= CB - OC

= 4 - $\sqrt{3^{2} + 2^{2}}$

= 4 - $\sqrt{13}$

Maximim value of |z| = OA = 4 + $\sqrt{13}$

The absolute difference between the maximum and minimum values of |z| is 2 $\sqrt{13}$

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