A complex number is a type of number that combines a real part and an imaginary part. It is expressed in the form 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 numbers are used in various fields, including engineering, physics, and mathematics. Complex numbers can be represented graphically on a plane called the complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. This representation helps visualize operations like addition and multiplication of complex numbers. They also play a crucial role in solving equations that do not have real solutions, such as quadratic equations.