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FP2: Roots of Unity

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if this is true for when Z^n=1 then why, for z^10=1, does k= +/-1,+/-2,+/-3, +/-4 and 5? I have the general solution as cos kpi/5+isin kpi/5. I would be grateful for any explanation😅

Posted from TSR Mobile

(edited 7 years ago)

Reply 1

Protoxylic

Original post by Mr Pussyfoot

if this is true for when Z^n=1 then why, for z^10=1, does k= +/-1,+/-2,+/-3, +/-4 and 5? I have general solution as cos kpi/5+isin kpi/5. I would be grateful for any explanation😅

Posted from TSR Mobile

Those values of k are the principal solutions

Reply 2

Mr Pussyfoot

Original post by Protoxylic

Those values of k are the principal solutions

So wouldn't the solutions be all the numbers -1<k<10?

Posted from TSR Mobile

Reply 3

Protoxylic

Original post by Mr Pussyfoot

So wouldn't the solutions be all the numbers -1<k<10?

Posted from TSR Mobile

You can either have all the values of k for which the the solutions have argument (0,2pi) or (-pi,pi) these tend to be the principal domains. Technically any domain with period 2pi, but the principal tends to be the above two.