MathDB

8

Part of 1998 National High School Mathematics League

Problems(1)

Complex Number

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

3/9/2020
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________.
complex numbersgeometryparallelogram