The imaginary unit, denoted as i, is a mathematical concept used to extend the real number system. It is defined as the square root of -1, which means that i² = -1. This allows for the creation of complex numbers, which are expressed in the form a + bi, where a and b are real numbers. Complex numbers, which include the imaginary unit, are essential in various fields such as engineering, physics, and applied mathematics. They enable the solution of equations that do not have real solutions and are used in signal processing, control theory, and quantum mechanics, among other applications.