Maths-
General
Easy
Question
If 
=1 and arg (z1 z2) = 0, then
- z1 = z2
- |z2|2 = z1z2
- z1z2 = 1
- none of these.
The correct answer is: |z2|2 = z1z2
Let z1 = r1( cosq1 + i sinq1) then 
Þ |z1| = |z2| Þ|z1| = |z2| = r1 .
Now arg (z1 z2) = 0 Þ arg( z1) + arg(z2) = 0 Þ arg(z2) = – q1
Therefore, z2 = r1 ( cos(–q1) + i sin(–q1)) = r1( cosq1 – i sinq1) = 
Þ 
= 
= z1 Þ|z2|2 = z1 z2 .
Hence (b) is the correct answer.
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