A complex series is a sequence of complex numbers that can be summed to produce a limit. Each term in the series is a complex number, which consists of a real part and an imaginary part. Complex series are often used in mathematics and engineering to analyze functions and signals, particularly in fields like signal processing and control theory. One common example of a complex series is the Fourier series, which represents periodic functions as sums of sine and cosine functions. Complex series can converge or diverge, depending on the behavior of their terms, and understanding their convergence is essential for many applications in mathematics and physics.