When multiplying two complex numbers in polar form, all you need to do is multiply the moduli and sum the arguments. Let
z = 4 (cos(2π/3) + i sin(2π/3))
w = 2 (cos(π/3) + i sin(π/3))
Then
|z| = 4
arg(z) = 2π/3
|w| = 2
arg(w) = π/3
and so
zw = |z| |w| (cos(arg(z) + arg(w)) + i sin(arg(z) + arg(w)))
zw = 8 (cos(π) + i sin(π))
zw = -8
