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Question

The image of the complex number 2i3+i, in the straight line z(1+i)=¯z(i1), where z is a complex number, is/are
  1. 1i2
  2. 1+i2
  3. i(i+1)2
  4. 11+i


Solution

The correct options are
B 1+i2
C i(i+1)2
D 11+i
2i3+i=(2i)(3i)9+1=55i10
=12i2
i.e.(12,12) is given point.
and z(1+i)=¯z(i1)
Let z=x+iy
(z+¯z)+i(z¯z)=0
z+¯z2+iz¯z2=0
x+i(iy)=0
xy=0y=x

Reflection of (12,12) with respect to y=x is (12,12)
i.e. 12+i2=1+i2
=i2+i2=i(i+1)2
=i(1+i)22(1+i)=i(1+i2+2i)2(1+i)
=i21+i=11+i

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