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thrtythreeforty • today at 5:10 AM • 2 replies • view on HN

Here's another good reason to think in turns: it turns Euler's formula from this Eldritch Terror:

    e^(i*x) = cos(x) + i*sin(x)
into something you can kinda understand by staring at the complex plane:

    -1^(2x) = cost(x) + i*sint(x)
Credit to justinpombrio for this: https://news.ycombinator.com/item?id=32986869

Replies

judofyr • today at 6:24 AM

I'm confused. How is this simpler? Is there something in (-1)^(2x) that can easily understood by staring at the complex plane? It seems mostly that you've gotten rid of "e", but one of the goals of Euler's formula IMO is to explain what "e^(i …)" means so I'm not sure how this variant is useful.

lefra • today at 7:08 AM

Now define exponentiation by a non-integer.