Write the expression in the standard form a bi Squareroot 3

Write the expression in the standard form a + bi. [Squareroot 3 (cos 55 degree + i sin 55 degree)^6 [Squareroot 3 (cos 55 degree + i sin 55 degree)^6 = (Simplify your answer, including any radicals. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expression.)

Solution

(3(cos55^o+i sin55^o))⁶

=(3)⁶(cos(6*55)^o+i sin(6*55^o))

=27(cos(330)^o+i sin(330^o))

=27((3_/2)+i (-1_/2))

=((273)_/2) - i (27_/2)