The History of Imaginary Numbers

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The History of Imaginary Numbers

The origin of imaginary numbers dates back to the ancient Greeks. Although, at

one time they believed that all numbers were rational numbers. Through the years

mathematicians would not accept the fact that equations could have solutions that were

less than zero. Those type of numbers are what we refer to today as negative numbers.

Unfortunately, because of the lack of knowledge of negative numbers, many equations

over the centuries seemed to be unsolvable. So, from the new found knowledge of

negative numbers mathematicians discovered imaginary numbers.

Around 1545 Girolamo Cardano, an Italian mathematician, solved what seemed to

be an impossible cubic equation. By solving this equation he attributed to the acceptance

of imaginary numbers. Imaginary numbers were known by the early mathematicians in

such forms as the simple equation used today x = +/- ^-1. However, they were seen as

useless. By 1572 Rafael Bombeli showed in his dissertation “Algebra,” that roots of

negative numbers can be utilized.

To solve for certain types of equations such as, the square root of a negative

number ( ^-5), a new number needed to be invented. They called this number “i.” The

square of “i” is -1. These early mathematicians learned that multiplying positive and

negative numbers by “i” a new set of numbers can be formed. These numbers were then

called imaginary numbers. They were called this, because mathematicians still were

unsure of the legitimacy. So, for lack of a better word they temporarily called them

imaginary. Over the centuries the letter “i” was still used in equations therefore, the name

stuck. The original positive and negative numbers were then aptly named real numbers.

What are Imaginary Numbers?

An imaginary number is a number that can be shown as a real number times “i.”

Real numbers are all positive numbers, negative numbers and zero. The square of any

imaginary number is a negative number, except for zero. The most accepted use of

imaginary numbers is to represent the roots of a polynomial equation (the adding and

subtracting of many variables) in one variable. Imaginary numbers belong to the complex

number system. All numbers of the equation a + bi, where a and b are real numbers are a

part of the complex number system.

Imaginary Numbers at Work

Imaginary numbers are used in a variety of fields and holds many uses. Without

imaginary numbers you wouldn’t be able to listen to the radio or talk on your cellular

phone. These type of devices work by receiving and transmitting radio waves. Capacitors

and inductors are used to make circuits that are used to make radio waves.
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