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Question

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

A
4
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B
5
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C
6
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D
7
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Solution

The correct option is B 5
Given,

|2z6+5i|

=2z3+52i

=2z3+2i2i+52i

=2z32i+92i

wkt

|z1||z2||z1+z2||z1|+|z2|

|z1+z2|=|z1||z2|

z32i+94i=|z32i|92i

=292=52

2z32i+92i=|2z6+5i|=2×52=5

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