First slide

De-moivre's theorem

Question

The value of $\sum_{k = 1}^{6} (\sin \frac{2 k π}{7} - i \cos \frac{2 k π}{7}) =$

Easy

A

$- 1$
B

$0$
C

$- i$
D

$i$

Solution

$\sum_{k = 1}^{6} (\sin \frac{2 k π}{7} - i \cos \frac{2 k π}{7}) = - i \sum_{k = 1}^{6} (\cos \frac{2 k π}{7} + i \sin \frac{2 k π}{7})$
$= - i \sum_{k = 1}^{6} e^{\frac{i 2 π k}{7}} = - i [- 1 + \sum_{k = 0}^{6} e^{i \frac{2 k π}{7}}]$

$= - i [- 1 + 0] = i$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App