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Minimum Tangent Angle for Complex Inequality

2300ExpertComplex NumbersGeometryOptimization

HMMT November 2022 · 2022

Consider the set $S$ of all complex numbers $z$ with nonnegative real and imaginary part such that $$ |z^{2}+2| \leq |z| $$ Across all $z \in S$, compute the minimum possible value of $\tan \theta$, where $\theta$ is the angle formed between $z$ and the real axis.
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