Question

How do I multiply complex numbers in polar form?

Answer 1

To explain this, I will name two generic complex.
`c_1 = a*cis(alpha)` and `c_2 = b*cis(beta)`

The product between `c_1` and `c_2` is:
`ab*cis(alpha)cis(beta) =`
`ab*(cos(alpha)+isin(alpha)) (cos(beta)+isin(beta)) =`
`ab*({cos(alpha)cos(beta)-sin(alpha)sin(beta)} +`
`{i(sin(alpha)sin(beta)+cos(alpha)sin(beta)}) =`
`ab*{cos(a+b)+isin(a+b)}`//

Therefore, we can assume that the product of the two complex numbers `c_1` and `c_2` can be generaly given by the form above.

Ex.:
`(2*cis(pi)) * (3*cis(2pi)) = 6*cis(3pi) = 6*cis(pi)`

Hope it helps.