From a physics class, I remember the statement "the Fourier Transform of a plane wave is the delta distribution", e.g. for the unitary transform, $\widehat{e^{ibx}} = \sqrt{2 \pi}\ \delta (k - b)$. I understand that these plane waves are not "square integrable", so we do not formally consider them. ** But I wonder if it is acceptable to use this on homework / quiz / test?**

For example, when trying to calculate the transform of a function like $f(x) = e^{-\alpha \left|x\right|}\cos \beta x$, I want to consider the exponential and the $\cos$ functions separately, find their Fourier Transforms, and then convolute. The $\cos$ will give these delta distributions by Euler's Identity, and the convolution will be easy.

Cheers,

Jack