Complexity! (3)

Algebra Level 3

If \(z\) is a complex number of unit modulus whose argument is \(\theta\), find \(\arg \left( \dfrac{1+z}{1+\bar{z}} \right)\).

Notations:

  • \(\bar{z}\) denotes the conjugate of \(z\).
  • \(\arg (\cdot)\) denotes the argument of a complex number.

For more problems on complex numbers, click here.

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