Use De Moires Theorem to find the indicated power Write the

Use De Moires Theorem to find the indicated power, Write the result in rectangular for a+bi

1) (2 square root of 3-2i)^5

Solution

(2sqrt3 -2i)⁵

r=sqrt(12 +4)=4

theta=tan^-1(-2/2sqrt3)=11pi/6

4(cos(11pi/6)-sin(11pi/6))⁵

4⁵(cos (55pi/6)-i sin (55pi/6)) = 1024(-sqrt3/2 -i 1/2)= -512sqrt3 - 512 i