JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z \) is a complex number of unit modulus and argument \(\theta\), then \({\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)\) equals.
- A \( - \theta \)
- B \(\frac{\pi }{2} - \theta \)
- C \(\;\theta \)
- D \(\;\pi - \theta \)
Answer & Solution
Correct Answer
(C) \(\;\theta \)
Step-by-step Solution
Detailed explanation
\(|z|=1,\) arg \(z=\theta \quad z=e^{i \theta}\) \(\bar{z}=\frac{1}{z}\) \(\arg \left(\frac{1+z}{1+\frac{1}{z}}\right)=\arg (z)=\theta\)
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