# convolution of two exponential signals with imaginary numbers

I can solve problems without imaginary numbers, but when exponential contain imaginary numbers, I can't solve the problem. For example, $$x(t)=e^{3jt}+e^{4jt}$$, $$y(t)=(e^{-3t}-e^{-4t})u(t)$$ (where $$j$$ is imaginary number and $$u(t)$$ is step function) I can't calculate $$x(t)*y(t)$$ easily.

In other problem that I can handle, I just easily calculate the integrals and make the answers, but with these imaginary numbers on the exponentials, I can't calculate the integrals even with the help of the calculator

can somebody help me?

• Could you clarify the source of your confusion? In theory, you just apply the convolution formula, just as in the real case. – MBaz Mar 25 at 18:14
• @MBaz First of all I can't solve this type of problem that contains an imaginary number so I just bring one case of the problem. If someone can show me how the way to solve that kind of problem, I can solve other problems on my own. – lin ki Mar 25 at 18:20
• @linki why can't you solve it. It's just numbers. What's the problem here? you need to be a bit more specific, please :) – Marcus Müller Mar 25 at 18:23
• @MarcusMüller yeah I edited few lines that make the question more specific. But the main problem is, I can't calculate this convolution :( – lin ki Mar 25 at 18:31
• so, you know what the convolution is as a formula? Can you write down the formula? Why can't you just do exactly the same as for real exponents? – Marcus Müller Mar 25 at 18:33