Complex Number Calculator

This calculator works with two complex numbers, returning their sum, their product, and the modulus and argument of the first, the essential operations for anyone studying or applying complex numbers. A complex number has a real part and an imaginary part, written a plus bi, where i is the square root of minus one. Far from being merely abstract, complex numbers are indispensable in electrical engineering, signal processing, control systems, quantum physics and advanced mathematics, where they neatly describe oscillations, waves and rotations. The basic operations have simple rules but are easy to slip on by hand. Adding combines the real parts and the imaginary parts separately. Multiplying uses the distributive rule, remembering that i squared equals minus one, which mixes the parts in a way that catches people out. The modulus is the distance of the number from the origin in the complex plane, found like a vector magnitude, and the argument is the angle it makes, which together give the polar form used so widely in engineering. You enter the real and imaginary parts of each number, and the calculator returns the sum, the product, the modulus of the first number, and its argument in degrees. The results update as you type, so you can explore how the parts interact, particularly the sign changes in multiplication. Use it to check homework, to verify an engineering calculation, or to convert between rectangular and polar thinking. The arithmetic is exact for your inputs, with the modulus and argument rounded for display.

For complex numbers a+bi and c+di. Multiplication uses i squared = -1. Modulus and argument are rounded for display.