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Question

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

A
θ
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B
π2θ
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C
θ
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D
πθ
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Solution

The correct option is C θ
z¯¯¯z=1 [ Since, |z|=1 ]
¯¯¯z=1z ---- ( 1 )
Now,
arg(1+z1+¯¯¯z)
arg⎜ ⎜ ⎜1+z1+1z⎟ ⎟ ⎟

arg⎜ ⎜ ⎜1+zz+1z⎟ ⎟ ⎟ [ From ( 1 ) ]

arg⎜ ⎜ ⎜1+z1+zz⎟ ⎟ ⎟

arg(z)

θ


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