If-cos-2pi-5-i-sin-2pi-5-then-find-the-value-of-2-3-4-

Question Number 19435 by Tinkutara last updated on 11/Aug/17

If α = \cos \frac{2 π}{5} + i \sin \frac{2 π}{5}, then find the

value of α + α^{2} + α^{3} + α^{4} .

Answered by ajfour last updated on 11/Aug/17

\underset{r = 1}{\sum^{4}} α^{r} = \frac{α (1 - α^{4})}{1 - α} = \frac{e^{i 2 π / 5} - e^{i 2 π}}{1 - e^{i 2 π / 5}} = - 1 .

Commented by Tinkutara last updated on 11/Aug/17

Thank you very much Sir!