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Q.

Let z be a complex number satisfying |z|3+2z2+4z¯8=0, where z denotes the complex conjugate of z. Let 
the imaginary part of z be nonzero.
Match each entry in List-I to the correct entries in List-II.

 List-I  List-II 
P) |z|2 is equal to1)12
Q)|zz¯|2 is equal to2)4
R)|z|2+|z+z¯|2 is equal to3)8
S)|z+1|2 is equal to4)10
  5)7
 PQRS
1)1354
2)2135
3)2451
4)2354

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a

2

b

1

c

3

d

4

answer is B.

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Detailed Solution

Let z=x+iy
x2+y23+2x2y2+4x8+i(4xy4y)=0
If x=11+y2321y2+48=0
1+y2=21+y2y2+1=4y2=3z=(1+i3)( or )(1i3)z2=4,|zz¯|2=12,|z|2+|z+z¯|2=8|z+1|2=7P2,Q1,R3,S5

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