Complex numbers are numbers that contain both a real and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part, with i being the imaginary unit equal to √(-1).
Complex numbers can be represented on a graph known as the complex plane. The horizontal axis represents the real part and the vertical axis represents the imaginary part. The numbers are plotted as points on this plane.
Complex numbers are used in various fields of mathematics, including algebra, geometry, and calculus. They are particularly helpful in solving equations that involve square roots of negative numbers and in representing oscillating quantities such as electrical currents and sound waves.
To add or subtract complex numbers, simply add or subtract the real parts and the imaginary parts separately. To multiply complex numbers, use the FOIL method and then combine like terms. To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the denominator and simplify.
Yes, complex numbers have various real-world applications. They are used in electrical engineering for analyzing alternating currents and in physics for representing the wave nature of particles. They are also used in economics for modeling supply and demand curves, and in signal processing for analyzing audio and video signals.