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<p>A slightly bizarre sidelight: there's no law against a modulating signal made up of complex numbers.
In this case, cos is no longer bounded, so the output can peak at anything, but
we still get FM-like spectra.  <img src="pix/fmeq54.png" alt="J=I">, where "I" is
the modified Bessel function,
so if our index is purely imaginary, we can expand cos(wc + bi sin wm)t as
</p>

<img class="indented" src="pix/fmeq55.png" alt="i case">

<p>If our index is a + bi, we get
</p>

<img 