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**How to define Laplace transforms and their complex values?**

## Homework Statement

the tutorial question asks to compute the Laplace transform of cos(3t)

__without using linearity theorem__

it then asks where the laplace transform is defined in terms of complex values

## Homework Equations

L(f(t))=s/s^2+a^2

## The Attempt at a Solution

now it's been a while since I did Laplace but what I get just from looking at the standard Laplace table is s/[(s^2)+9] obviously, is there something else I'm missing here in terms of linearity or?

I must also confess that i don't recall complex values relating to Laplace other than the fact that 's' is complex in the sense that it gives a+bi for instance. It's not defined just for {R} is it?

any pointers you could give me on this would be just great guys and girls! thanks a lot.

-chief10

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