Complex Number - Overview

Overview

Complex numbers allow for solutions to certain equations that have no real solution: the equation

has no real solution, since the square of a real number is either 0 or positive. Complex numbers provide a solution to this problem. The idea is to extend the real numbers with the imaginary unit i where, so that solutions to equations like the preceding one can be found. In this case the solutions are −1 ± 3i. In fact not only quadratic equations, but all polynomial equations in a single variable can be solved using complex numbers.