File:LCost minus3plus12i.png

Contour, $\cos\left({t}\right) e^{-\left({-3+12i}\right)t}$.

The integrand of $\mathcal{L} \left\{{\cos \left({t}\right)}\right\}\left({-3+12i}\right)$

The integral does not converge; the Laplace Transform does not exist for $s = -3+12i$.