Question

Let \( w \neq \pm 1 \) be a complex number. If \( |w| = 1 \) and \( z = \frac{w - 1}{w + 1} \), then \( \text{Re}(z) \) is equal to:

• A. \( 1 \)
• B. \( \frac{1}{|w + 1|} \)
• C. \( \text{Re}(w) \)
• D. \( 0 \)
• E. \( w + \bar{w} \)

Hint:

Geometrically, if $|w|=1$, then $z = \frac{w-1}{w+1}$ maps a point on the unit circle to the imaginary axis. This is a common transformation in complex analysis.

Answer 1

The Correct Option is D