Let λ1+λ2+...+λn=1 where λi>0 for i=1,2,...,n. If |ai|<1 and ω is – InterviewSolution

1.	Let λ1+λ2+...+λn=1 where λi>0 for i=1,2,...,n. If \|ai\|<1 and ω is a complex cube root of unity, then \|λ1a1ω+λ2a2ω2+...+λnanωn\| cannot exceed
Answer» Let $λ_{1} + λ_{2} + . . . + λ_{n} = 1$ where $λ_{i} > 0$ for $i = 1, 2, . . ., n$ . If $\| a_{i} \| < 1$ and $ω$ is a complex cube root of unity, then $\| λ_{1} a_{1} ω + λ_{2} a_{2} ω^{2} + . . . + λ_{n} a_{n} ω^{n} \|$ cannot exceed

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