Determine-the-poles-of-the-function-f-x-x-5-1-x-3-1-

Question Number 100943 by Ar Brandon last updated on 29/Jun/20

D etermine the poles of the function;

f (x) = \frac{x^{5} - 1}{x^{3} - 1}

Answered by mathmax by abdo last updated on 29/Jun/20

the poles are z with verify z^{3} - 1 = 0 and z \neq 1

z^{3} = 1 \Leftrightarrow z^{3} = e^{i (2 k π)} \Rightarrow z_{k} = e^{i \frac{2 k π}{3}} and k \in {1, 2} \Rightarrow the poles are

z_{1} = e^{\frac{i 2 π}{3}} and z_{2} = e^{\frac{i 4 π}{3}}

Commented by Ar Brandon last updated on 29/Jun/20

Thanks. I didn't understand the question.