A Purely Imaginary Ratio

★ 6/10complex numbers Extrema Completing the Square Trigonometric Identities

Problem

Let $z \in \mathbb{C}$ be such that $\dfrac{z-1}{z+1}$ is purely imaginary. Find the minimum of

\left|z^2 + z + 3\right|.

Answer

Solution

Difficulty	6/10
Topics	complex numbers, Extrema, Completing the Square, Trigonometric Identities

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