Nov 102014
 

(Note: I lied. This will be my first “neural dump.” I began writing about Euler’s Formula, but felt what follows was worthy of its own post and a better foundation for what will follow when I tackle Euler.)

Complex numbers arose from the fact that there is no solution for x in the equation x^2 = -1 in \mathbb{R}, the set of real numbers.

Early mathematicians being the devil-may-care mavericks that they were, were all like, “Screw it. Let’s just invent a new number. We’ll just call this number i and say that the solution is x = i.” Or, in other words, this new number i they imagined up (see what I did there) is equal to \sqrt{-1}.

    \[i = \sqrt{-1}\]

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