Changes

::Mathematically, you can derive this formula by doing standard mathematics (i.e., calculating series) in the field '''R'''[x]/[x²+1]. --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 18:08, 16 August 2015 (EDT)

::Mathematically, you can derive this formula by doing standard mathematics (i.e., calculating series) in the field '''R'''[x]/[x²+1]. --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 18:08, 16 August 2015 (EDT)

*Defining ''i'' as the solution of <math>x^2-1=0</math> is conceptually not more difficult than defining "-1" as the solution of <math>x + 1 = 0</math>. The latter problem has baffled mankind for centuries! ''i'' and ''-1'' are both somewhat quite imaginary - or at least imaginative - entities!

*x: <math>x</math>

*''Definition'' - ''Theorem'' - ''Proof'': that's somewhat how modern mathematics work, so, you cannot complain that Euler started with a definition.

*x^2: <math>x^2</math>

*<math>e^{i\phi} = \cos \phi + i\sin \phi </math> follows quite  straightforward by using <math>e^x = \sum_{n=0}^\infty \frac{x^n}{n!}</math>.

*x^2_1: <math>x^2_1</math>

--[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 14:32, 17 August 2015 (EDT)

*\frac{x}{y}: <math>\frac{x}{y}</math>

*\hat{x}: <math>\hat{x}</math>