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ISI B.Math(Hons.) Admission Test 2009 Problem 1

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April 9, 2012
complex numbers

Problem Statement

Let x,y,zx,y,z be non-zero real numbers. Suppose α,β,γ\alpha, \beta, \gamma are complex numbers such that ∣α∣=∣β∣=∣γ∣=1|\alpha|=|\beta|=|\gamma|=1. If x+y+z=0=αx+βy+γzx+y+z=0=\alpha x+\beta y+\gamma z, then prove that α=β=γ\alpha =\beta =\gamma.
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