Question

How to use DeMoivre's Theorem to find the indicated power of (sqrt 3 - i)^6 ?

Answer 1

`-64`

Explanation:

`sqrt(3) - i = 2(sqrt(3)/2 - i/2) = 2 (cos(-30°) + i*sin(-30°))`
`= 2*e^(-i * pi/6)`
`=> (sqrt(3) - i)^6 = (2*e^(-i*pi/6))^6 = 64*e^(-i*pi)`
`= 64*(cos(-180°) + i*sin(-180°))`
`= 64*(-1 + i * 0)`
`= -64`