Euler's Formula in College Algebra

Once complex numbers are introduced in a College Algebra/PreCalculus course, why not discuss Euler’s formula? Especially the equation $e^{\pi i}+1=0$, that looks good on a T-shirt. A full proof is out of question, but the power series definitions of the exponential and trigonometric functions provide a narrow, but walkable path up to the summit. With a computer algebra system it is easy to demonstrate how the approximations work, just by entering a few terms of the infinite sums. Actually, it is also a good advertisement for a Calculus course, good practice of the sigma notation (handy in Statistics).

Experience shows that the complex exponential function breaking up into the trigonometric functions does have a dramatic effect on anyone following the argument.

This Handout (PDF) contains the argument, presentable in one class, close to the end of the semester.

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