It is often attributed to Swiss Mathematician Leonhard Euler. Interestingly enough, this is nothing but a statement about rotation!

2^{3} is a shorthand way of writing 2 × 2 × 2. But this is very very different from what means. Mathematicians use this trick over and over again. They overload notations. In fact is a shorthand way of writing an infinite series.

How can we connect infinite series with rotation? Basically, 1 is not 1! 1 is (1, 0). A point in fact. Then what is i? i is a shorthand for writing (0, 1). So when you add 1 + 2 π i , you are in fact ‘adding’ (1, 0) + 2 π (0, 1) = (1, 2 π ).

Food for thought

How do you add many many many points (in fact infinitely many) to get rotation?

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