Inverse Transform for Complex Poles In Section 9–4 we learned that complex poles occur in conjugate pairs and that for simple poles the partial fraction expansion of F(s) will contain two terms of the form FðsÞ ¼ . . .

k s þ a  jb

þ k s þ a þ jb

þ . . .

Show that when the complex conjugate residues are written in rectangular form as k ¼ a þ jb and k

¼ a  jb the corresponding term in the waveform f(t) is f ðtÞ ¼ . . . þ 2eat ½a cosðbtÞ  b sinðbtÞ þ . . .