Complex Analysis explores the properties and applications of complex numbers and functions, emphasizing their geometric interpretations and analytical techniques.
Complex numbers and functions are at the heart of signal processing. They allow the representation of oscillating signals and make analysis much simpler.
Signals can be written as sums of sines and cosines using complex exponentials, thanks to Euler’s formula. This makes transformations like the Fourier transform possible, which breaks down signals into their frequency components.
In electrical engineering, alternating current (AC) circuits are analyzed using complex numbers to represent voltages and currents with phases and amplitudes.
Analyzing a radio signal using the Fourier transform and complex exponentials.
Solving for currents and voltages in an AC circuit using complex impedance.