A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined by the property that i² = -1. In this expression, a is called the real part and b is referred to as the imaginary part.
For example, in the complex number 3 + 4i, 3 is the real part and 4 is the coefficient of the imaginary part. Complex numbers are a crucial extension of the real numbers and enable us to solve equations that do not have solutions within the set of real numbers, such as the equation x² + 1 = 0.
In practical applications, complex numbers are widely used in fields such as engineering, physics, and applied mathematics, especially when dealing with waveforms, vibrations, and electrical circuits.