Expressing exponential functions

Can someone provide me a list of the important complex exponential functions. For example, $\cos (at) = \large \frac{e^{iat} +e^{-iat}}{2}$. I am trying to find the laplace transformation for a given function by definition and it helps to know how to convert a $cosat$ or $sinat$ to a exponential function. I googled it, but couldn't find anything.

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What do you mean by "complex exponential functions"? –  Qiaochu Yuan Dec 7 '12 at 0:05
@QiaochuYuan like for an example , expressing cosat in terms of complex exponential functions $\cos (at) = \large \frac{e^{iat} +e^{-iat}}{2}$ –  Q.matin Dec 7 '12 at 0:07
@QiaochuYuan The question tells me to take the laplace transform by definition for cosat and they expressed the cosat in terms of those exponential function to simplify the integration calculation. –  Q.matin Dec 7 '12 at 0:09
What is 'cosat'? Doesn't it want to be $\cos(at)$ where, I guess, $a$ is constant and $t$ is the variable? –  Berci Dec 7 '12 at 0:12
@Berci yes , sorry for not clarifying that. –  Q.matin Dec 7 '12 at 0:14