In information theory, complex numbers are typically not used as commonly as they are in fields such as physics and engineering. However, they do have some applications in the field, such as in the representation of certain types of signals, such as quadrature amplitude modulation (QAM) and phase-shift keying (PSK).

Complex numbers can be used to represent the amplitude and phase of a signal, which can be useful for certain types of modulation. QAM and PSK are examples of digital modulation schemes that use the phase of a signal to convey information. These modulation schemes are used in many communication systems, such as digital television and wireless communication systems.

Additionally, complex numbers also appear in some advanced topics in information theory such as the theory of error-correcting codes and the study of channel capacity. In these topics, complex numbers are used to represent the probability amplitudes of quantum states, which are necessary to study the properties of quantum channels and quantum error-correcting codes.

In summary, complex numbers and especially the imaginary unit, i, are not commonly used in information theory, but they do have some applications in certain areas such as modulation, signal processing, and quantum information theory.