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Question

A rectangle of maximum area is inscribed in the circle |z−3−4i|=1. If one vertex of the rectangle of 4+4i, then another adjacent vertex of this rectangle can be-

A
2+4i
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B
3+5i
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C
3+3i
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D
33i
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Solution

The correct options are
B 3+3i
C 3+5i
Clearly, the rectangle with maximum area is a square.
Let the adjacent vertex be z.
Then,
3+4i(z)(3+4i)(4+4i)=e±iπ/2
(by rotation about center)
3+4iz=±i(1)
z=3+4i±i=3+5i or 3+3i

365809_117218_ans.PNG

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