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Q.

If z1=a+ib and z2=c+id are complex numbers such that |z1|=|z2|=1 and Re(z1z2¯)=0 such that   w1=a+ic  and w2=b+id  are two complex numbers. then which of following  is INCORRECT

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a

|w1|=1

b

|w2|=2

c

Re(w1w2¯) =0

d

None of these

answer is B.

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Detailed Solution

Re(z1z2¯)=0⇒ac+bd=0 also  a2+b2=1and  c2+d2=1hence d=0Also, a=0 and b=±1. using these we get |w1|=|w2|=1   and Re(w1w2¯)=0
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