Technologically Embodied
Geometric Functions
Euler’s Formula

Return to the complex plane unit description.

In the 1740’s Euler applied his limit definition of the function `e^x` to imaginary values of x. For reasons that will become clear, we generally write this function as `e^(i theta)` rather than `e^(i x)`. In this activity you will use the limit definition to construct the value of this function for different values of `theta`.

Use pages 1 through 5 to review Euler’s definition of `e`, to extend the definition to find `e^x`, and finally to write a limit expression for `e^(i theta)`.

Use page 6 to construct the expression for which you need to find the limit. Construct it initially for `n = 5` and then for `n = 10`. Experiment with different values of `theta`.

Use the prepared construction on page 7 to use larger values of `n` without having to do every single multiplication. Also use this page to experiment with different values of `theta`.


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Update History:

18 October 2016: Created this page.
15 November 2016: Clarified some elements of pp. 1–5, and added text describing the purpose of the pages of the sketch.
Still need to add hint videos.