1. Tardigrade
  2. Question
  3. Mathematics
  4. If α= e i 2π/11 then Real (α+α2+α3+α4+α5) equals to :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $\alpha= e ^{i 2\pi/11}$ then Real $\left(\alpha+\alpha^2+\alpha^3+\alpha^4+\alpha^5\right)$ equals to :

Complex Numbers and Quadratic Equations

Solution:

Real $\left(1+\alpha+\alpha^2+\ldots \ldots . .+\alpha^{10}\right)=0 $
$\Rightarrow 1+$ Real $\left(\alpha+\alpha^2+\ldots \ldots \alpha^5\right)+$ Real $\left(\alpha^6+\alpha^7+\ldots \ldots .+\alpha^{10}\right)=0$
$\Rightarrow 2 $ Real $\left(\alpha+\alpha^2+\ldots \ldots . \alpha^5\right)=-1$
$ \Rightarrow \left(\alpha+\alpha^2+\alpha^3+\alpha^4+\alpha^5\right)=-1 / 2$