Complex and Imaginary Numbers
1. Introduction
The purpose of this research paper is to introduce the topic of “Complex and Imaginary Numbers” and its applications. I chose the topic “Complex and Imaginary Numbers” because I am interested in mathematics that is hard to be pictured in your mind, unlike geometry or equations.
An imaginary number is the square root of a negative number. That is why they are called imaginary, what René Descartes called them, because he thought such a number could not exist. In this paper, I will discuss how complex numbers and imaginary numbers were discovered, the interesting math of complex numbers, and how they are used in other areas of mathematics and science. Complex numbers are applied in engineering, control theory and improper integrals to take the place of certain imaginary values, as well as to simplify some explanations.
2. THe Concept
2.1 History of imaginary numbers
Long ago in ancient Greece, there was a society of mathematicians called Pythagoreans who believed the only numbers were natural numbers and positive rational numbers (Rusczyk 357). Later, Hippasus discovered irrational numbers such as√2, then 0 and negative numbers were introduced. This completes the real numbers set, but mathematicians at that time have not even thought of the set of imaginary numbers yet. The first appearance of complex numbers was made by Heron of Alexandria in the 1st AD (Complex Numbers-Wikipedia, the free encyclopedia). He merely replaced the inside of the square root as its positive, thinking he made an error. It was not until 1545 they were really used in mathematics when Cardano published “Ars Magna”, where he mentioned imaginary numbers. Later Bombelli set rules for arithmetic of imaginary and complex numbers in his book “Algebra”. Then, Euler assigned the letter “i” to denote the square root of -1. At the time of its discovery, many mathematicians like Descartes thought imaginary numbers to be useless and fictitious.
2.2 The mathematics of complex and
The purpose of this research paper is to introduce the topic of “Complex and Imaginary Numbers” and its applications. I chose the topic “Complex and Imaginary Numbers” because I am interested in mathematics that is hard to be pictured in your mind, unlike geometry or equations.
An imaginary number is the square root of a negative number. That is why they are called imaginary, what René Descartes called them, because he thought such a number could not exist. In this paper, I will discuss how complex numbers and imaginary numbers were discovered, the interesting math of complex numbers, and how they are used in other areas of mathematics and science. Complex numbers are applied in engineering, control theory and improper integrals to take the place of certain imaginary values, as well as to simplify some explanations.
2. THe Concept
2.1 History of imaginary numbers
Long ago in ancient Greece, there was a society of mathematicians called Pythagoreans who believed the only numbers were natural numbers and positive rational numbers (Rusczyk 357). Later, Hippasus discovered irrational numbers such as√2, then 0 and negative numbers were introduced. This completes the real numbers set, but mathematicians at that time have not even thought of the set of imaginary numbers yet. The first appearance of complex numbers was made by Heron of Alexandria in the 1st AD (Complex Numbers-Wikipedia, the free encyclopedia). He merely replaced the inside of the square root as its positive, thinking he made an error. It was not until 1545 they were really used in mathematics when Cardano published “Ars Magna”, where he mentioned imaginary numbers. Later Bombelli set rules for arithmetic of imaginary and complex numbers in his book “Algebra”. Then, Euler assigned the letter “i” to denote the square root of -1. At the time of its discovery, many mathematicians like Descartes thought imaginary numbers to be useless and fictitious.
2.2 The mathematics of complex and
Cited: Rusczyk, Richard. Introduction to Algebra. 2nd Edition. Alpine: Aops Incorporated, 2009. Print. "Complex Number -." Wikipedia, the Free Encyclopedia. N.p., n.d. Web. 16 Nov. 2012. . “Complex Numbers.” Math is Fun. N.d. N.d. Web. 16 Nov. 2012. Dawkins, Paul. “Algebra-Notes” -.”Paul’s Online Math Notes”, n.d. Nov. 2012. Joyce, David. “Complex Numbers”-.”Dave’s Short Course on Complex Numbers” Clark University, 1999. Dec. 2012