Write the given complex number in the standard form z a bi

Write the given complex number in the standard form z = a + bi. Do not use a calculator. Z = cos 5 pi/3 + i sin 5 pi/3 ______________

z=cos(5pi/3) +isin(5pi/3)

cos(5pi/3)=cos(2pi - pi/3) and sin(5pi/3)=sin(2pi - pi/3)

cos(2pi - theta) = cos theta and sin(2pi-theta)=-sin theta

therefore

cos(2pi-pi/3)=cos(pi/3) and sin(2pi - pi/3)=-sin(pi/3)

z= cos pi/3 - i sin pi/3

z= 1/2 - isqrt3/2