Roots of unity question (1 Viewer)

porcupinetree · Mar 29, 2015

http://imgur.com/jghkxRx

For some reason, I'm stuck on part ii: I know that beta is equal to p^3 + p^5 + p^6, but I cannot find a way to "justify your answer". It's probably really obvious but I just can't see it.

By the way, I'm fine with all other parts of the question.

InteGrand · Mar 29, 2015

porcupinetree said:
http://imgur.com/jghkxRx

For some reason, I'm stuck on part ii: I know that beta is equal to p^3 + p^5 + p^6, but I cannot find a way to "justify your answer". It's probably really obvious but I just can't see it.

By the way, I'm fine with all other parts of the question.

The reason is that, by the conjugate root theorem, $\beta = \overline{\alpha} = \overline{\rho + \rho ^2 + \rho ^4} = \overline{\rho} + \overline{\rho ^2} + \overline{\rho ^4}=\rho ^6 + \rho ^5 + \rho ^3$ as $\overline{\rho ^k} = \rho ^{7-k}$ .

porcupinetree · Mar 29, 2015

InteGrand said:
The reason is that, by the conjugate root theorem, $\beta = \overline{\alpha} = \overline{\rho + \rho ^2 + \rho ^4} = \overline{\rho} + \overline{\rho ^2} + \overline{\rho ^4}=\rho ^6 + \rho ^5 + \rho ^3$ as $\overline{\rho ^k} = \rho ^{7-k}$ .

Ah, thankyou. Knew it was right under my nose

Roots of unity question (1 Viewer)

porcupinetree

not actually a porcupine

InteGrand

Well-Known Member

porcupinetree

not actually a porcupine

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