Question:medium
If \( |z| = 5 \) and \( w = \frac{z-5}{z+5} \), then \( \text{Re}(w) \) is equal to:
If \( |z| = 5 \) and \( w = \frac{z-5}{z+5} \), then \( \text{Re}(w) \) is equal to:
Show Hint
The mapping \( w = \frac{z-k}{z+k} \) maps the circle \( |z|=k \) onto the imaginary axis (where \( \text{Re}(w)=0 \)). This is a fundamental property of Möbius transformations.
Updated On: May 1, 2026
- \( 0 \)
- \( \frac{1}{25} \)
- \( 25 \)
- \( 1 \)
- \( -1 \)
Show Solution
The Correct Option is A
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