$z_1= \cos(4\pi/3) + i\sin(4\pi/3)$
$z_2= \cos(π/3) + i\sin (π/3)$
I want to find out $z_1z_2$.
I know that $(x +iy)(u + iv$) = $(xu - yv) + i(xu + yv)$
So I want to simplify $\cos(4π/3)\cos(π/3) - \sin(4π/3)\sin(π/3)] + i[\cos(4π/3)\cos(π/3) + \sin(4π/3)\sin(π/3)]$
First of, is my formula correct and second, how would I multiply sin or cos functions?
Any assistance would be greatly appreciated.