Question

If \( f(z) = \frac{1 - z^3}{1 - z} \), where \( z = x + iy \) with \( z \neq 1 \), then \( \mathrm{Re}(f(z)) = 0 \) reduces to

• A. \( x^2 + y^2 + x + 1 = 0 \)
• B. \( x^2 - y^2 + x - 1 = 0 \)
• C. \( x^2 - y^2 - x + 1 = 0 \)
• D. \( x^2 - y^2 + x + 1 = 0 \)
• E. \( x^2 - y^2 + x + 2 = 0 \)

Hint:

Always simplify complex fractions using algebraic identities before substituting \(z = x+iy\).

Answer 1

The Correct Option is D