First of all I would like to write that the invention of i is the second most beautiful thing in mathematics.
The first being trigonometric functions.
The man stood up. Defying and balancing gravity. And thereby creating y axis. And the cause for a symbol i (of complex numbers). It is not easy for a common man to "see" i. Just as he doesn't realise he can walk or stand on two legs.
The invention of i is of the 17th, 18th century.
It was Euler who used square root of (-1) in his expressions. He did not use i though. But square root of (-1).
It was Carl Gauss who advocated the use of i.
Well there are so many advantages.
To the power (x + iy) is no problem. As it is to the power x into to the power iy.
Addition is no problem. Just simple commutative law.
Subttraction no problem. Commutative.
Division is a little tough. But one can multiply with complex conjugate both the numerator and the denominator. In fact I believe conjugates are a reality and a person sort of experiences conjugates. Eating at first is a happy experience. But eating changes to unhappiness. Exercising at first is a happy experience. But exercises changes to unhappiness. So I believe. So I think.
My learning shall continue. I am interested in putting practical analogy to functions.
I read Prof. Hardy saying that Mathematics is more of an art like painting.
I believe in it.
(Please also refer to
complex numbers.)
