Complex Numbers
Geometry of Complex Numbers, Maxima and Minima
jee_adv_2026_mock_p1
Grade 12
Question:
If z is a complex number satisfying |z - 1| = 1, then the maximum value of |z^2 - z + 1| is:
Step-by-Step Solution
Key Concept: |z - 1| = 1 represents a circle centered at (1, 0) with radius 1. Parametrize z = 1 + e^{iθ}.
Step 1: Let z = 1 + e^{iθ}. Step 2: z^2 - z + 1 = (1 + e^{iθ})^2 - (1 + e^{iθ}) + 1 = 1 + e^{iθ} + e^{2iθ}. Step 3: The maximum occurs at θ = π/3, giving value 3.
Correct Answer: C
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