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Q.

Let Z1,Z2,Z3,Z4 be distinct complex numbers satisfying |Z1|=|Z2|=|Z3|=|Z4|=1  such that, 

0arg(Z1)<arg(Z2)<arg(Z3)<arg(Z4) and

arg(Z2)+arg(Z4)arg(Z1)arg(Z3)=π

then the value of 

|Z1Z3(Z1Z3)(Z2Z4)|2|(Z1Z3)(Z2Z4)|2 is

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a

1

b

2

c

3

d

4

answer is A.

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Detailed Solution

detailed_solution_thumbnail

arg(Z2)+arg(Z4)arg(Z1)arg(Z3)=π=arg(Z2Z4Z1Z3)=π

Z2Z4Z1Z3=k (where k>0)

k=|z2z4z1z3|=1z2z4=z1z3

|z1z3|2+|(z1z3)(z2z4)|2z¯1z¯3(z1z3)(z2z4)

=1{(z1z3)(z2z4)z1z3+(z1z3)(z2z4)z2z4}=1

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