File:LCost minus3plus12i.png

Contour, $\map \cos t e^{-\paren {-3 + 12 i} t}$.

The integrand of $\laptrans {\map \cos t} \paren {-3 + 12 i}$

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