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Question

If z is a complex number of unit modulus and argument θ, then arg(1+z1+¯z)=

A
π4
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B
θ
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C
π2θ
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D
2θ
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Solution

The correct option is B θ
|z|=1z¯z=1¯z=1z
Now, 1+z1+¯z=1+z1+1z=z
arg(1+z1+¯z)=arg(z)
and we are given that arg(z)=θ

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