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 are useful in various fields, including engineering, physics, and applied mathematics, as they help solve equations that do not have real solutions. The introduction of the imaginary unit enables a broader understanding of mathematical concepts and enhances problem-solving capabilities.