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AIEEE 2003

JEE Main 2003 Mathematics question on Complex Numbers and Quadratic Equations

If ∣z∣=1|z| = 1 and w=z−1z+1w = \dfrac{z-1}{z+1} (where, z≠−1z \neq -1), then Re(w)\text{Re}(w) is
  1. A.
    0
  2. B.
    1∣z+1∣2\dfrac{1}{|z+1|^2}
  3. C.
    ∣1z+1∣⋅1∣z+1∣2\left|\dfrac{1}{z+1}\right| \cdot \dfrac{1}{|z+1|^2}
  4. D.
    2∣z+1∣2\dfrac{\sqrt{2}}{|z+1|^2}
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Correct option: A

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