An imaginary number is a type of number that can be expressed as a real number multiplied by the imaginary unit i, which is defined as the square root of -1. Imaginary numbers are used in mathematics to solve equations that do not have real solutions, such as x² + 1 = 0. When combined with real numbers, imaginary numbers form complex numbers, which are expressed in the form a + bi, where a is the real part and b is the imaginary part. Complex numbers have applications in various fields, including engineering, physics, and computer science.