Complex numbers are a type of number that includes a real part and an imaginary part. They are 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 can be added, subtracted, multiplied, and divided, just like real numbers. These numbers are useful in various fields, including engineering, physics, and mathematics. They help in solving equations that do not have real solutions and are essential in understanding concepts like electrical circuits and wave functions in quantum mechanics.