HSC Stuff > HSC Mathematics Extension 2

Debunking \(\sqrt{ab} \neq \sqrt{a}\sqrt{b}\)

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lzxnl:

--- Quote from: dantraicos on December 21, 2018, 02:52:47 am ---Should note: although I took a more technical approach, I actually more enjoy Rui's intuitive approach to this idea about accessing points in the complex plane :)
I couldn't agree more. I think complex analysis is so interesting. I can't wait to formally take it at uni!!

--- End quote ---
Hahahaha complex analysis is great. At the cost of having more requirements for differentiability, you get so much more from it. No more infinitely differentiable functions that are not equal to their Taylor series. Any function differentiable once in a neighbourhood around any point is differentiable infinitely many times about that point and admits a Taylor series. Isn't that beautiful?
Bounded non-constant functions can't be differentiable everywhere. Every differentiable everywhere function (that's not constant) blows up in some direction.

And even better, you can now solve sin(x) = 2.

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