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