MathDB
Complex Number

Source: 1998 National High School Mathematics League, Exam One, Problem 8

March 9, 2020
complex numbersgeometryparallelogram

Problem Statement

Complex number z=cos⁡θ+isin⁡θ(0≤θ≤π)z=\cos\theta+\text{i}\sin\theta(0\leq\theta\leq\pi). Points that three complex numbers z,(1+i)z,2z‾z,(1+\text{i})z,2\overline{z} refer to on complex plane are P,Q,RP,Q,R. When P,Q,RP,Q,R are not collinear, PQSRPQSR is a parallelogram. The longest distance between SS and the original point is________.
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