## Mathmatics or "it's all Greek to me"

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Reply #31 –

These three contradictory excuses are very fine whlie you simply apply complex analysis to ease calculus/notation. There shold be one but good reason WHY

Nope. Why use decimal numbers? Sometimes they are useful for this, sometimes they are useful for that. There is no need to dig up one big reason why you should always use decimal numbers -- indeed, there is none such, as there are applications where they are utterly useless.

Have a look at the Mandelbrot set (edit: just google it, you'll recognize the shape). The algebra behind is elegant in complex numbers, but I can describe it just as precise without mentioning "complex numbers" or "imaginary numbers". In reality I'd be doing precisely the same -- I would just have to define a vector-valued function of two variables, a function which does the same as the complex square. Should I or should I not invoke complex numbers?

The science of mathematics -- and crafts of applied mathematics, even -- is full of analogous examples. Adding additional machinery may or may not be useful to a given problem. Even assuming it is useful, then teaching or learning that additional machinery has an effort cost which may or may not be outweighted by its usefulness.