3} = 1$

Asked Feb 11 '22 at 08:16

Active Feb 11 '22 at 08:16

Viewed 27 times

I want to calculate the 3rd cyclotomic polynomial $\phi_3$.

So according to the definition we have: $\phi_3 = (x - e^{2 \pi\cdot i / 3})(x - e^{2 \pi\cdot i \cdot 2/ 3})$

I seem to have a basic misunderstanding of polar coordinates:

$e^{2 \pi\cdot i / 3} = (e^{2 \pi\cdot i}) ^{2/ 3} = 1^{2/3} = 1$ which is clearly wrong. But why can't you do that? It follows the formulas we had...

asked Feb 11 '22 at 08:16

mathematics-and-caffeine

2

e^2pi/3 = (e^2pi)^(2/3) why? (e^x)^y = e^xy – CuriousIndeed Feb 11 '22 at 08:20
2

Also, $(a^{b})^{c}=a^{bc}$ is not valid for complex numbers. – Kavi Rama Murthy Feb 11 '22 at 08:28
This is the same error as in https://math.stackexchange.com/q/281528/42969 – can we close this as a duplicate? – Martin R Feb 11 '22 at 08:29
Yes it does answer my question, thanks – mathematics-and-caffeine Feb 11 '22 at 08:46

$e^{2 \pi\cdot i / 3} = (e^{2 \pi\cdot i}) ^{2/ 3} = 1^{2/3} = 1$

0 Answers0