First slide

De-moivre's theorem

Question

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

Easy

A

-1
B

0
C

–i
D

i

Solution

$\prod_{k = 1}^{6} (\sin \frac{2 k π}{7} - i \cos \frac{2 k π}{7}) = (- i) {^{6} \prod}_{k = 1}^{6} (\cos \frac{2 k π}{7} + i \sin \frac{2 k π}{7}) = (- 1) 1 = - 1$

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