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Question

If |z|=1, z±1, then z1z2 lies on

A
a line not passing through the origin.
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B
a circle.
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C
on the real axis
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D
on the imaginary axis
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Solution

The correct option is D on the imaginary axis
Given |z|=1, z±1
Let ω=z1z2
ω=zz¯¯¯zz2 (|z|=1z¯¯¯z=1)ω=1¯¯¯zz
As ¯¯¯zz is purely imaginary, so
ω lies on the imaginary axis.

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