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# Why were imaginary numbers created?

Updated: 4/28/2022

Wiki User

12y ago

Originally, they were created so that every polynomial would have a solution. For example, the polynomial xÂ² - 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 = xÂ² - 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 xÂ² + 1 = 0. If you graph y = xÂ² + 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 iÂ² = -1. Now this number i can be used to solve xÂ² + 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).

Wiki User

12y ago