Write the expression in the standard form a bi squareroot 3

Write the expression in the standard form a + bi. [squareroot 3 (cos 5 pi/6 + i sin 5 pi/6)]^4 -9/2 - 9 squareroot 3/2 i -9/2 + 9 squareroot 3/2 i -9 squareroot 3/2 - 9/2 i -9 squareroot 3/2 + 9/2 i

Solution

(sqrt3(cos 5pi/6   + i sin 5pi/6))⁴ = (sqrt3⁴(cos (20pi/6) + isin(20pi/6) ))

                                                        = 9(-1/2 -isqrt3/2)

                                                         = -9/2 - 9sqrt3i/2

Hence the correct option is A