Multiplication of two complex numbers in exponential form

Question

I am trying to understand how the multiplication of 2 complex numbers work.

I don't understand how i should behave when there are complex exponentials with different signs.

Here i've created an example in which there are both cases.

$$(e^{i600πt} - e^{-i600πt})(e^{i400πt} + e^{-i400πt})$$

What would the result of $(e^{-i600πt})(e^{i400πt})$ be?

Thanks!

Answer 1

$(e^{-i600πt})(e^{i400πt})=e^{i(-600+400)πt}=e^{-200i\pi t}=\cos{({-200\pi t})}+i\sin{({-200\pi t})}$