Imaginary numbers are a type of number that extends the concept of real numbers. They are based on the imaginary unit, denoted as i, which is defined as the square root of -1. This means that i² = -1. Imaginary numbers are often 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, expressed in the form a + bi, where a is the real part and b is the imaginary part. Complex numbers are useful in various fields, including engineering, physics, and computer science, as they help model and solve problems involving oscillations, waves, and electrical circuits.