Find roots of a complex variable such that

Leonard Montes

Leonard Montes

Answered question

2022-04-15

Find roots of a complex variable such that 1+ωm+ω2m++ω(n1)m=0
I need some help understanding the intuition behind the following question:
Consider the root of zn=1 given by ω=cos2πn+isin2πn . For which integers m is 1+ωm+ω2m++ω(n1)m=0?

Answer & Explanation

Mey9ci0

Mey9ci0

Beginner2022-04-16Added 14 answers

If wm1 then using the geometric sum we get
wnm1wm1=0
which's always true. So m should be: mnk, kZ

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