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Question

If one of the vertices of the square, inscribed in the circle |z1|=2, is 2+3i, then other vertices of the square are

A
i3
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B
(13)+i
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C
(3+1)i
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D
i3
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Solution

The correct options are
B (13)+i
C (3+1)i
D i3
The given circle is |z1|=2 where z0=1 is the centre and 2 is radius of the circle. z1 is one of the vertices of the square inscribed in the given circle.

Hence all the other vertices can be obtained by rotating the z1 about z0 by ±π2,π. Thus,
z2z0=(z1z0)eiπ/2
z21=(2+i31)(i)
z2=i3+1
z2=(13)+i
similarly z4=(3+1)i
and z3z0=(z1z0)eiπ
z3=z0(z1z0)=i3

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