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Markus Klein
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Markus Klein
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  • 94

Is $e^{i\pi}+1=0$ a good motivation for introducing $e$ or $i$? Why (not)?

Most mathematicians would agree that $$e^{i\pi}+1=0$$ is one of the most impressive formulas.

Imagine your students have just learned about the definition of $e$ or $i$ (just assume it's $e$, normally $i$ comes later in curricula); $\pi$ should be known for sure at that point.

Is it a good motivation for the new quantity (here $e$ or $i$) for the students if you tell them about the formula above (and maybe short explaining the unknown quantity) to emphasize the importance of the new variable ($e$ or $i$)? Or is such a thing distracting or even unhelpful since you overload the students with stuff they don't know at that point (and maybe don't care)?