MathDB
Complex Number

Source: 1991 National High School Mathematics League, Exam One, Problem 2

February 26, 2020
complex numbers

Problem Statement

a,b,ca,b,c are three non-zero-complex numbers, and ab=bc=ca\frac{a}{b}=\frac{b}{c}=\frac{c}{a}, then the value of a+b−ca−b+c\frac{a+b-c}{a-b+c} is (ω=−12+32i\omega=-\frac{1}{2}+\frac{\sqrt3}{2}\text{i}) (A)1(B)±ω(C)1,ω,ω2(D)1,−ω,−ω2\text{(A)}1\qquad\text{(B)}\pm\omega\qquad\text{(C)}1,\omega,\omega^2\qquad\text{(D)}1,-\omega,-\omega^2
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