MathDB
Complex Number

Source: 1999 National High School Mathematics League, Exam Two, Problem 2

March 10, 2020
complex numbers

Problem Statement

Let a,b,ca,b,c be real numbers, z1,z2,z3z_{1},z_{2},z_{3} be complex numbers such that {∣z1∣=∣z2∣=∣z3∣=1z1z2+z2z3+z3z1=1\begin{cases} \displaystyle|z_1|=|z_2|=|z_3|=1\\ \displaystyle\frac{z_{1}}{z_{2}}+\frac{z_{2}}{z_{3}}+\frac{z_{3}}{z_{1}}=1\\ \end{cases} Find ∣az1+bz2+cz3∣|az_{1}+bz_{2}+cz_{3}|.
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