If is a complex number such that

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If zz is a complex number such that ∣z∣≥2|z| \ge 2 , then the minimum value of ∣z+(12)∣\left| z + \left(\frac{1}{2}\right) \right| , is (1) is strictly greater than 52\frac{5}{2} (2) is equal to 52\frac{5}{2} (3) is strictly greater than 32\frac{3}{2} but less than 52\frac{5}{2} (4) lies in the interval (1,2)(1, 2)

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