There's a great lecture discussing this from Robin Wilson:https://www.youtube.com/watch?v=1VL2fl1_wB8 …
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What an amazing lecture. It covers all the history. Thanks.
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ln not log, surely?
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ln is used for real numbers logarithm, for complex nos log is used...
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It's close enough for me, give it to Cotes.
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How do you come about this formula from examining the surface area of an allipsoid?
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same question. How "investigating the surface area of an ellipsoid", leads to the expression: log(cosφ + isinφ) = iφ ??
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Now set pi as phi
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Thank you for that. I've been calling it de Moivre's identity all these years. Now I find he never quite wrote that formula. (What's in a name? I dunno, but Cotes' has a greater claim.) https://en.m.wikipedia.org/wiki/De_Moivre's_formula …
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If anyone wonders the proof, write e^ix as Taylor series.
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