MathDB

6

Part of 2011 ISI B.Stat Entrance Exam

Problems(1)

P6: Complex numbers: 6|n and (alpha)^n=1

Source:

3/31/2013
Let α\alpha be a complex number such that both α\alpha and α+1\alpha+1 have modulus 11. If for a positive integer nn, 1+α1+\alpha is an nn-th root of unity, then show that α\alpha is also an nn-th root of unity and nn is a multiple of 66.