Complex numbers

Complex numbers are numbers that extend the traditional number system to include solutions to equations like \(x^2 + 1 = 0\), which have no real solutions. They consist of two parts: a real part and an imaginary part, written as \(a + bi\), where \(a\) is real, \(b\) is real, and \(i\) is the imaginary unit defined by \(i^2 = -1\). Complex numbers are useful in fields like engineering, physics, and signal processing for solving problems involving oscillations, waves, and systems with two interconnected quantities, offering a complete framework for analyzing phenomena that can't be described using only real numbers.