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Question

If |z|=1 and ω=z1z+1 (where, z1), then Re (ω) is


A

0

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B

1|z+1|2

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C

1z+1.1|z+1|2

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D

2|z+1|2

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Solution

The correct option is A

0


Since,|z|=1 and omega=z1z+1z1=ωz+ωz=1+ω1ω|z|=|1+ω||1ω||1ω|=|1+ω| [|z|=1]
On squaring both sides,we get
1+|ω|22Re(ω)=1+|ω|2+2Re(ω)
using |z1±z2|2=|z1|2+|z2|2±2Re(¯z1z2)]4Re(ω)=0Re(ω)=0


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