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August 15th, 2016, 08:43 AM   #1
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Euler's Indentity

Could mathematics ever be described as beautiful? Every once in a while, an equation comes along which links together, most beautifully, two or more areas of knowledge that may have seemed hitherto unrelated. So it is with Euler's Identity.

This video explores what Euler's Identity is, a little of the history of the man who proposed it, and how a number, which can only be imagined, has spawned its very own field of mathematics: Complex Numbers.

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August 15th, 2016, 02:47 PM   #2
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Hardy answered the question in the affirmative.

Anyway. Your video was very neat. Thanks. My wife understood it, and she is somewhat agnostic about negative numbers and would certainly never soil her hands with one.

Questions. I don't think Euler "invented" i. Were not the algebraists of the late 16th century using the concept when solving cubics? Did Euler initiate the use of i as representation?

First comment. When you gather like terms, reals and complex, you need ... in both sums. Picky picky.

And $(-i)^2 = (-\ i) * (-\ i) = (-\ 1)i * (-\ 1)i = 1 * i^2 = -\ 1 = (i)^2.$

So i is not the only number that, when squared, equals minus 1. Picky, picky.

Second comment. I might have worked out the term to the fifth power.

Despite these little cavils, I do like this, and thank you for providing it.
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