z 32 2i31 Squareroot 3iSquareroot 3 i2Solutionz 32 2i31s

z = 3(2 - 2i)^3/(-1 - Squareroot 3i)(-Squareroot 3 + i)^2

z =3(2 -2i)^3/(-1-sqrt3i)(-sqrt3 +i)^2

(-1-sqrt3i)(-sqrt3 +i)^2 = (-1 - sqrt3i)(3 -1 -2isqrt(3)) = (1-sqrt3i)(2 -2isqrt3)

= 2 -2isqrt3 - 2isqrt3- 6

= -4 -4isqrt3

Polar form : -4 -4isqrt3 = 8e^i*4pi/3

(2- 2i) = 2sqrt2e^7pi/4 = 2^(3/2)e^(7pi/4)

(2-2i)^3 = 2^(9/2)e^(i*21/4)

z = 3*2^(9/2)e^(i*21/4)/8e^i*4pi/3

= 3*2^(9/2 -3)e^i(21/4 - 4/3)

z =3*2^(3/2)e^i(47/3)