Laplace Transform/Graphical Interpretation/Examples/Cosine t of -3 + 12 i

Example of Graphical Interpretation of Laplace Transforms
From Laplace Transform of Cosine, $\map {\laptrans {\map \cos t} } {-3 + 12 i}$ does not exist.

Notice how the contour spirals outward as $t$ increases without bound, never settling at a "stable point":


 * LCost minus3plus12i.png