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Question

If z is any complex number satisfying |z32i|2, then minimum value of |2z6+5i| is___

A
5
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B
2.5
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C
4.5
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D
9
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Solution

The correct option is A 5
Given |z32i|2
which represents a circular region with centre (3, 2) and radius 2.
Now |2z6+5i|=2z(352i)
=2× distance of z from P
(where Z lies in or on the circle)
Also min distance of z from P=52
Minimum value of |2z6+5i|=5

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