A complex variable is a type of variable that can take on values in the form of complex numbers, which consist of a real part and an imaginary part. A complex number is typically expressed as a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit, defined as the square root of -1. Complex variables are used in various fields, including mathematics, engineering, and physics, to model phenomena that cannot be adequately described using only real numbers. In mathematics, the study of complex variables is known as complex analysis. This branch focuses on functions that depend on complex variables and explores their properties, such as continuity, differentiability, and integrability. Complex analysis has important applications in areas like fluid dynamics, electrical engineering, and quantum mechanics, where it helps solve problems involving wave functions and potential fields.