If z is a complex number of unit modulus and argument θ , then arg(1+z/1+z) equals: - Mathematics MCQ JEE Main 2026 | ExamTest.live

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If z is a complex number of unit modulus and argument θ, then arg (\frac{1 + z}{1 + z ˉ}) equals:

Solution & Step-by-step Explanation

Given ∣ z ∣ = 1 \Rightarrow z \overset{z}{ˉ} = ∣ z ∣^{2} = 1 \Rightarrow \overset{z}{ˉ} = \frac{1}{z} .Substitute \overset{z}{ˉ} in the expression: \frac{1 + z}{1 + z ˉ} = \frac{1 + z}{1 + \frac{1}{z}} = \frac{1 + z}{\frac{z + 1}{z}} = z Thus, arg (\frac{1 + z}{1 + z ˉ}) = arg (z) = θ .

Try it yourself before checking the explanation above.

If z is a complex number of unit modulus and argument θ, then arg (\frac{1 + z}{1 + z ˉ}) equals:

\frac{\pi}{2} - \theta

\theta

\pi - \theta

-\theta

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