Imaginary Numbers

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/