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.