The equation z = x + iy represents a complex number, where z is the complex number itself, x is the real part, and iy is the imaginary part. Here, i is the imaginary unit, defined as the square root of -1. Complex numbers are used in various fields, including mathematics, engineering, and physics, to solve problems that cannot be addressed using only real numbers. In this representation, x and y can take any real values, allowing for a two-dimensional plane known as the complex plane. The horizontal axis represents the real part, while the vertical axis represents the imaginary part. This visualization helps in understanding operations like addition, subtraction, and multiplication of complex numbers.