- #1
ggb123
- 25
- 0
I'd like to figure out why
[tex] f(x) = x^n - r e^{i \theta} = \prod_{j = 0}^{n - 1} ( x - r^{1/n} e^{i \theta / n} e^{2 \pi i j / n} ) [/tex],
as I've seen it used as an identity in a few courses but I cannot figure it out. Could somebody shed some light? I understand they are the roots of the function, but I'd like some kind of analytic description.
Thanks a lot!
[tex] f(x) = x^n - r e^{i \theta} = \prod_{j = 0}^{n - 1} ( x - r^{1/n} e^{i \theta / n} e^{2 \pi i j / n} ) [/tex],
as I've seen it used as an identity in a few courses but I cannot figure it out. Could somebody shed some light? I understand they are the roots of the function, but I'd like some kind of analytic description.
Thanks a lot!