Complex numbers › The complex plane › Extremes of the modulus

Maximum modulus on a locus

High school · ●●○○○ 20 pts

Given a complex number zz such that z−iz−1\frac{z-\mathrm{i}}{z-1} is a purely imaginary number, where i\mathrm{i} is the imaginary unit, find the maximum value of ∣z∣|z|. Round to two decimal places.

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