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If z1 = a + ib and z2 = c + id are complex  numbers such that |z1| = |z2|=1 and Re=0, then the pair of complex numbers w1 = a + ic and w2 = b + id satisfies – (1985 - 2 Marks)
  • a)
    |w1|= 1
  • b)
    |w2|= 1
  • c)
  • d)
    none of these
Correct answer is option 'A,B,C'. Can you explain this answer?
Verified Answer
If z1 = a + ib and z2 = c + id are complex numbers such that |z1| = |z...
(a, b, c) z1 = a + ib   and  z2 = c + id.
ATQ  |zi|2 = |z2|2 = 1
⇒​ a2 + b2 =1   and   c2 + d2 = 1. ....(1)
Also Re = 0 ⇒​ ac + bd=0
 = α(say)  ....(2)
From (1) and (2), we get
b2 α2 + b2 = c2α2 + c2 ⇒​ b2 = c2;
Similarly   a2  = d2
∴      
and    
Also Re = ab + cd = (bα) b + c (-cα)
= α(b2 -c2 )=0
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If z1 = a + ib and z2 = c + id are complex numbers such that |z1| = |z2|=1 and Re=0, then the pair of complex numbers w1 = a + ic and w2 = b + id satisfies – (1985 - 2 Marks)a)|w1|= 1b)|w2|= 1c)d)none of theseCorrect answer is option 'A,B,C'. Can you explain this answer?
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