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Question

If |z|=1 and z±1, then all the values of z1z2 lie on


Your Answer
A
a line not passing through the origin
Your Answer
B
|z|=2
Your Answer
C
The X - axis
Correct Answer
D
The Y - axis

Solution

The correct option is B The Y - axis
Let z=cosθ+i sinθz1z2=cosθ+sinθ1(cos2θ+i sin2θ)=cosθ+i sinθ2sin2θ2i sinθcosθ=cosθ+i sinθ2i sinθ(cosθ+i sinθ)=i2sinθ
Hence, z1z2 lies on the imaginary axis i.e. Y-axis.

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