write the expression in the standard form abi 12 root32 i10

write the expression in the standard form a+bi. (-1/2 - root(3)/2 i)^10

(-1/2 - root(3)/2 i)^10

Appy De-moivres formula : z^n = r^n(cos(n*x) + i*sin(n*x) )

r = sqrt( (1/4 + 3/4) = 1

x = tan^-1(sqrt3) = pi +pi/3 = 4pi/3

z^10 = 1^10[ cos(10*4pi/3) +i*sin(10*4pi/3)]

= cos(40pi/3) + i*sin(40pi/3)

= -1/2 + i*(-sqrt3/2)

= -1/2 - i*sqrt3/2