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

1 Answer
MattyMatty
Feb 27, 2018

#-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#

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