# The History of Imaginary Numbers

Length: 1077 words (3.1 double-spaced pages)

Rating: Excellent

#### Essay Preview

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.

MLA Citation:
"The History of Imaginary Numbers." 123HelpMe.com. 25 Jan 2020
<https://www.123helpme.com/view.asp?id=125457>. ## Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

## The History of Imaginary Numbers Essay

- 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....   [tags: Papers]

Free Essays
1077 words (3.1 pages)

## Not All Conspiracies are Imaginary Essay

- Not All Conspiracies are Imaginary Almost as an article of faith, some individuals believe that conspiracies are either kooky fantasies or unimportant aberrations. To be sure, wacko conspiracy theories do exist. There are people who believe that the United States has been invaded by a secret United Nations army equipped with black helicopters, or that the country is secretly controlled by Jews or gays or feminists or black nationalists or communists or extraterrestrial aliens. But it does not logically follow that all conspiracies are imaginary....   [tags: Conspiracy Theory Theories]

Research Papers
5740 words (16.4 pages)

## Numbers and Morals Essay

- Numbers and Morals We learn that any argument is stronger by numbers than without the numbers. If the numbers and percentages are inappropriate, we are automatically reacting against the causes, and if it is not, we wait for the time that it is. Dose we make a correct choice when our decision affected by numbers that come from market and economics researches. Are we free to choose what is right. Dose market brings to us freedom as the Ronald Reagan and Margaret Thatcher believe “that markets, not government, held the key to prosperity and freedom?”(Sandel 6) Are we supposed to consider moral values in our market solutions or not....   [tags: Moral Values, Market Solutions, History]

Research Papers
897 words (2.6 pages)

## Essay about history of algebra

- Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking were considered to be two separate parts of math and were not unified until the mid 17th century....   [tags: essays research papers]

Research Papers
1187 words (3.4 pages)

## Man and the Environment in David Malouf’s Novel, An Imaginary Life Essay

- In David Malouf’s novel An Imaginary Life, one of the most prevalent influences on the characters’ lives is the particular environment in which they are placed. Malouf explores the issues of the interrelationship between man and his natural environment, and the impact that changes in environment have on human personality. Through the characterisation of Ovid and the Boy, the effects of setting and physical surroundings are fully explored, and consequently issues such as isolation, conformity to society and the development of culture, including education and language, are discussed....   [tags: An Imaginary Life]

Research Papers
1963 words (5.6 pages)

## The History of Mathematics Essay example

- ... Around 1950BC, The Moscow papyrus was written, which gave details of Egyptian geometry. Around 1800BC, the Babylonians start using the multiplication tables. The Babylonians also solve the linear and quadratic equations and pulls together the tables of square and cube roots. Around 1400BC, the decimal number system with no zeroes started to be used in China. Around 127BC, Hipparchus figured out the equinoxes and calculated the length of the year to about 6.5 minutes of the correct value, started the understanding of trigonometry (A Mathematical Chronology,2014)....   [tags: geometry, fractions, numbers]

Free Essays
641 words (1.8 pages)

## Trafficking in Numbers: The Social Construction of Human Trafficking Data, by David Feingold

- In today’s world, numbers and statistics play an undeniable role in shaping our perception of the world, and quantification has become a universal tool to support claims and provide necessary evidence. Such cases are especially predominant in the fields of politics and media. People nowadays seem to automatically accept numbers and mindlessly repeat them with an unquestionable air of authority and validity, without considering the importance of examining the methodology behind them and the source that produced them....   [tags: Statistics, Deriving Numbers]

Research Papers
1519 words (4.3 pages)

## Buffy the Vampire Slayer: Colonial Imaginary & “Pangs” Essay

- Buffy the Vampire Slayer: Colonial Imaginary & “Pangs” The cult show, Buffy the Vampire Slayer has been often heralded as groundbreaking and feminist; however, the show is not without its faults. Throughout the show’s seven-year run, the cast was predominantly white, with little cultural diversity represented. Various episodes depict the colonial imaginary, from a hypersexual Incan princess who comes back to life to seduce men , to the primitive and aggressive African Slayer . Perhaps the episode most engrained with colonial imaginary is the Thanksgiving episode, “Pangs”....   [tags: TV Episode Review]

Research Papers
1025 words (2.9 pages)

## The History of Math Essay

- The History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions....   [tags: Mathematics Education Logic Numbers Essays]

Research Papers
4777 words (13.6 pages)

## Prime Numbers Essay

- Prime Numbers Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers. A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28....   [tags: Papers]

Research Papers
1205 words (3.4 pages)

### Popular Essays

In order to
determine the right values of capacitors and inductors to use in the circuits, designers
need to use imaginary numbers.
Another use of imaginary and complex numbers is in physics, quantum mechanics
to be exact. In quantum mechanics a big problem is to find the position of a particle.
Unfortunately, only the probability distribution of it’s position is possible to find. The
only way to calculate this is to use imaginary and complex variables.
Lastly, electrical engineers use imaginary numbers. However, instead of using “i”
in their equations they use “j.” This is because in the equations they commonly use, “i”
means current, so to represent imaginary numbers they use “j.”
Four Most Familiar Number Concepts
There are four of the most common numbers that we, the common person, know
about and can understand why they exist. At one point or another you might have used
one of these four concepts in your math classes. The first concept are Natural Numbers,
which are abstract numbers that answer questions, like “how many.” They are able to
describe sizes and sets. The second concept are Integers, they describe the relative sizes
between two sets. They answer questions, like “how many more does A have than B?”
Rational numbers are what describes ratios and fractions. For example you might tell
Karen that you ate 3/4 of an apple pie. This will let Karen know you ate three quarters out
of a four quarter pie. A real number is a number that will describe a measurement like
weight, length and fluid. However, in none of the four concept can you see the square
root of -1 fall into place. There exist a fifth concept which is referred to as a complex
number. As mentioned earlier a complex number equation = a+bi. It is a real number with
an imaginary number.
Throughout our lifetime, teachers have informed students that negative numbers
cannot be squared. With imaginary numbers we are able to do so. With a very simple
example it can be shown how this is true. With an equation like y = x^2+ 4x+29, we can
get the x intercept by using the quadratic equation. By following all appropriate steps you
will find out where the x intercepts are at. Roots are all places that a graph will touch the
x intercept. The quadratic equation = -b+- square root of b^2-4(a)(c)/ 2(a). Therefore,
x^2=a , 4x= b and 29 = c.
-4+- square root of 4^2 - 4(1)(29)

2(1)
-4+- square root of 16-116

2
-4+- square root of -100

2
-4 +-10i

2
=-2+-5i
The answer -2 +-5i, lets you know that it is a complex root, meaning that it does
not touch the x intercept. By graphing the equation y=x^2+4x+29, you will see the
parabolas location. This parabola will not touch the x intercept. This table will show you
how:
i^1=i i^4=1
i^2=-1 i^5=i
i^3=-i i^6=i
Complex Root and Complex Conjugate Root
This is an ongoing cycle that will help you solve problems that deal with i^n
power. Another amazing technique you can use is when you are given a complex root and
the complex conjugate root and you need to derive the equation by the root given and
complex root. A complex conjugate root is that exact opposite of a complex root. For
example if you are given one complex root of 2-5i, and you are asked to find the equation
you simply multiply 2-5i by the conjugate root of 2+5i. By using foil method you will
find out the equation. For example:
(2-5i) (2+5i) = 4+10i-10i-25i
elimination will give you
=-25i^2+4
you know i^2= -1
therefore
=-25(-1)+4
a negative times a negative equals a positive
=25+4=29
You then add the complex root (2-5i) with it’s complex conjugate root (2+5i).
2+5i
=2-5i
=4
This will let you know that your equation is y=x^2+4x+29 and you are
able to graph and see how and where the complex roots are located on the graph.
Making An imaginary Number A Real Number
You can multiply, add, divide , subtract and even take the square root of a
negative number. Like mentioned in the History of Imaginary Numbers, negative
numbers were not believed to be a valid answer. However, we know that a negative
number does have meaning and is a valid answer. A negative number will let us
determine many different things. We see them in our check books, when graphing, and
even when finding the expected number of a roulette game. Complex numbers can be
added to show you how they can become real numbers. For example:
5i^2 + 4i^2= 9i^4
9(1)=9
The answer is a real number that we obtained after adding it to imaginary numbers. You
can refer to the imaginary number cycle. It is known that i^4=1, nine is then multiplied by
1 to get a positive nine. Weather you get a negative or positive number they are real
numbers.
Conclusion
Imaginary numbers are in fact very real. They have common uses and very
intricate uses. Little does the average person know the imaginary number is one of the
oldest and greatest discoveries ever found.

Bibliography:

Bibliography

Dr. Anthony, “Ask Dr. Math” The Math Forum, 1994-2001.
http://forum.swarthmore.edu/dr.math/faq/faq.imag.num.html
(2001-March-15).

Mathews, John. Howell. “Complex Analysis,” 2000.
(2001-March-15).

Nahin, Paul. (1998). “An Imaginary Tale.” New Jersey: Princeton University Press.

Ross, Kelley. Ph.D.. “Imaginary Numbers,” 2000.
www.friesian.com/imagine.htm
(2001-April-4).

Snyder, Bill. Personal Interview. 20 April. 2001.

Spencer, Philip. “Do Imaginary Numbers Really Exhist?” University of Toronto
Mathematics Network, 1997.