Date: 10/11/97 at 15:32:34 From: Molly Darden Subject: Imaginary numbers Dear Dr. Math, I have a test in my Calculus class and my teacher told us that we would get a bonus point if we could tell her who invented the imaginary number. I have looked everywhere for the answer and I can't find it. If you could tell me, I would appreciate it. Thank you, Molly Darden
Date: 10/11/97 at 19:53:35 From: Doctor Anthony Subject: Re: Imaginary numbers There was no one person who invented imaginary numbers. They arise naturally when trying to solve some equations, and they gradually emerged as a new class of number as those working in this field explored their nature. Similar in a way to the slow acceptance that irrational numbers encountered when they first came on the scene. Cardan (1501-1576) and Tartaglia published the first solution by radicals of the cubic equation in 1545. One of the possible solutions (the irreducible case) involves a discriminant which is negative, and when this occurred, in those days, they would have to change to a trigonometric solution. However, some other workers like Rafael Bombelli (1526-1573) discovered that multiplying 'conjugate' complex numbers (these are of the form a+ib and a-ib) leads to a real answer a^2+b^2 and by degrees mathematicians began to discover the rules by which these strange numbers could be manipulated. They were geometrically established following the work of Jean Argand (1768- 1822). As a general rule, a new branch of mathematics is never the work of one man. Problems arise which create a pressure for new techniques in mathematics (such as the calculus independently invented by Newton and Leibnitz within a few years of each other) and it is very difficult to apportion credit as one could for the work of a playwright or author. To get the full story of imaginary (complex) numbers you would need to study the work of literally dozens of mathematicians. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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