Complex numbers are numbers that contain both a real and an imaginary part. They are represented in the form a + bi, where a is the real part and bi is the imaginary part with i being the imaginary unit, √(-1).
To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (1 + 4i) = (3 + 1) + (2 + 4)i = 4 + 6i.
To multiply complex numbers, use the FOIL method. For example, (3 + 2i)(1 + 4i) = 3 + 12i + 2i + 8i^2 = 3 + 14i - 8 = -5 + 14i.
To divide complex numbers, multiply both the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a + bi is a - bi. For example, (3 + 2i) / (1 + 4i) = (3 + 2i)(1 - 4i) / (1 + 4i)(1 - 4i) = (3 + 12i - 2i - 8i^2) / (1 + 16) = (11 + 10i) / 17.
Complex numbers can be used to represent and solve real-world problems involving alternating currents, electrical circuits, and signal processing. They can also be used in engineering, physics, and other sciences to model and analyze complex systems. In addition, complex numbers have applications in finance, economics, and statistics.
