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Question:

If z is a complex number of unit modulus and argument θ, then arg(1+z/(1+z̅)) equals: π/2−θ, θ, π−θ, −θ

π−θ

θ

π/2−θ

−θ

Solution:

Given:|z|=1⇒ z̅z=1
Now,1+z/(1+z̅)=1+z/(1+1/z)=1+z/(z+1)/z=1+z²/z+1=(1+z)
Hence, the argument is θ