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Hi, I'm just looking for a topic for my exploration and would like to do something to do with Eulers identity but I'm not quite sure what, maybe some applications , but I dont want to make it just look like a textbook explanation of it. It has to be suitable for the HL curriculum, does anyone have any ideas? Is investigating Eulers identity even a suitable topic?

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In the HL syllabus, you will go in depth about relationships among Euler's identity, complex numbers and trigonometry. It's a good starting point and you just start from there and develop more connections on your own or with help from reference materials. For reference, a simple derivation of the identity may take up 5-10 lines of math and few paragraphs. The IA is expected to be at least 6 pages so hopefully that give you an idea of how much more math you need.

Here's a video https://www.youtube.com/watch?v=-dhHrg-KbJ0 that looks at a geometric interpretation of taking exponents of imaginary numbers. It's bit below IB expectations but that gives you another starting point. 

 

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