Replacing

C with

C+

iD (

C,

D real) yields the wave packet formula:

Expanding out the exponent gives

, and so:

The first exponential is just a (complex) multiplying constant; the second controls the frequency, and the third shapes the amplitude.

Examining the second and third exponentials, we can see immediately that the wave packet has frequency

, and is centered at (i.e. peaks at)

.