Why were imaginary numbers created?

Answer 1

See related link for more information.

Originally, they were created so that every polynomial would have a solution. For example, the polynomial x² - 1 = 0 is a second order polynomial, so it should have 2 solutions. It does have 2 real solutions: 1 & -1. You can graph y = x² - 1 and see where the graph crosses the x-axis (these are the x coordinates that make y=0 and satisfy the equation). But what about x² + 1 = 0. If you graph y = x² + 1, it does not cross the x axis, but every polynomial is supposed to have a number solutions equal to the order {2nd order should have 2 solutions, 3rd order should have 3 solutions, etc.}

To handle polynomials like this, a number i was created such that i² = -1. Now this number i can be used to solve x² + 1 = 0. The solutions are x = i & -1. For many years, these numbers were considered just an imaginary concept, and for not much use until the work of Euler related them to sines and cosines. Now, imaginary and complex numbers are used to express the relationships between waves (in particular, electromagnetic waves and alternating current electricity).