To the ancient Greeks, numbers were only thought of to be rational. “The ancient Greeks once believed that all numbers were rational numbers; that is, that every number could be expressed as the ratio of two integers” (Engel, 1997). Therefore, if a solution came out to be irrational or negative, it was deemed useless. However, as time went on, these numbers that were thought to not exist were given a name, that name being negative. Furthermore, for many centuries there were quadratic equations that remained unsolved. Equations such as x2 = -1 did not have solutions. “These numbers

Imaginary numbers are used in a variety of fields and holds many uses. Without imaginary numbers, one wouldn’t be able to listen to the radio or use a cell phone. These types of devices work by receiving and transmitting radio waves. Capacitors and inductors are used to make circuits that are used to make radio waves. In order to determine the right values of the capacitors and inductors to use in the circuits, engineers need to use imaginary numbers. Another use of imaginary numbers is in physics, dealing with quantum mechanics. Finding the position of a particle using quantum mechanics is a very hard task. The only way to calculate this is to use imaginary and complex variables. Lastly, electrical engineers use imaginary numbers. However, instead of using i they use j. If they were to use i in their equations it would get confused with the already used variable of i to mean current.

An imaginary number is a number that can be shown as a real number multiplied by i. Real numbers are all positive numbers, negative numbers, and zero. Except for zero, the square of any imaginary number is a negative. Imaginary numbers are mostly used to represent roots of polynomial equations. Polynomial equations are equations with forms such as y = ax^2 + bx + c or any other equation involving variables to some degree greater than 1. However, if an equation has a degree that is one, than it is said to be linear. Imaginary numbers make up what mathematicians call the complex number system. Complex numbers are imaginary numbers with real numbers. They take the form a + bi where a is the real part, and b is imaginary.

The four most common number systems that can be understood why they exist. These would be the Natural numbers, the Rational numbers, Integers, and the Real numbers. So where exactly does the square root of -1 (which is

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