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ELI5: Why e^(2*pi*i) = 1. : explainlikeimfive - Reddit
https://www.reddit.com/r/explainlikeimfive/comments/3vnkoo/eli5_why_e2pii_1/
Dec 6, 2015 - 5 posts - ‎4 authors
Three imaginary numbers. Things get slightly more confusing with multiplication where, for instance, 2i*3i = (2*3)*(i*i) = 6*-1 = -6, but even that makes relative sense. Things get complicated, though, when we try taking exponents. What does it mean to multiply e by itself i times? To do that, we first need to ...Euler's identity - Wikipedia
https://en.wikipedia.org/wiki/Euler%27s_identity
Ï€ is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler.E^2*pi*i, where from? | Physics Forums - The Fusion of Science and ...
https://www.physicsforums.com › ... › Biology, Chemistry and Earth Homework
Sep 19, 2010 - The problem statement, all variables and given/known data. The problem at hand is that I don't understand wherefrom my text book got a certain term(e^(2*pi*i). It doesn't say. At least not as I understand it. The book says: 2. Relevant equations e^(z+2*pi*i) = e^z*e^(2*pi*i) = e^z*1 = e^z. From where does ...10 Sep 2009
complex analysis - $e^{2\pi i x} = (e^{2\pi i})^x$: What happens ...
https://math.stackexchange.com/.../e2-pi-i-x-e2-pi-ix-what-happens-if-x-is-rational
May 28, 2015 - Actually, when we are talking about complex numbers, the law of exponentiation is a little different from what we used to see in non-complex case. You can see this if you try to express your equality in trigonometric form, using Euler's formula. The paradoxes arising from exponentiation of complex numbers ...Question Corner -- Why is e^(pi*i) = -1? - University of Toronto
https://www.math.toronto.edu/mathnet/plain/questionCorner/epii.html
Jan 29, 1997 - So I put it into the calculator and it worked, but I have no idea why, because e to any power isnt supposed to be a negative number, and I thought pi was in ... By plugging in ix in place of x, you get e^(ix) = 1 + ix + i^2 x^2/2! + i^3 x^3/3! + i^4 x^Understanding e to the pi i - YouTube
https://www.youtube.com/watch?v=F_0yfvm0UoU
Mar 4, 2015 - Uploaded by 3Blue1Brown
Improved version here: https://youtu.be/mvmuCPvRoWQ The enigmatic equation e^{pi i} = -1 is usually ...Euler's formula: e^(i pi) = -1
https://cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node13.html
Feb 20, 1998 - which are the Taylor series expansion of the trigonometric sine and cosine functions respectively. From this, one sees that, for any real x,. exp(ix) = cos x + i sin x. Thus, we get Euler's famous formula. e^(pi i) = -1. and. e^(2 pi i) = e^0 = 1. One can also obtain the classical addition formulae for sine and cosine ...If [math]e^{2\pi i} = 1[/math], does this mean that [math]e^{2\pi ...
https://www.quora.com/If-e-2-pi-i-1-does-this-mean-that-e-2-pi-i-e-0-So-2-pi-i-0
If the sun rises tomorrow, does this mean that tomorrow's sunrise is the same phenomenon as that of today? So, tomorrow is today? Well, if [math]f(a) = f(b)[/e^(i*pi) = -1: pi = 0 - Math Forum - Ask Dr. Math
mathforum.org/library/drmath/view/53907.html
Jun 22, 2005 - Date: 10/17/97 at 11:29:15 From: John K. Koehler Subject: Weird tricks Dr. Math, I know that from a certain trig identity we get the equation e^(i*pi) = -1. I have been playing around with this equation and have found some disturbing things. I hope that you can help me. First: e^(2*i*pi) = 1 e^(-2*pi) = 1 (raised both sides to i ...15 Sep 2004
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If e^(i*pi)=-1, then - Khan Academy
https://www.khanacademy.org/questions/if-eipi-1...eipi2-121ei2pi-it/kafb_5399723
If e^(i*pi)=-1, then (e^(i*pi))^2=(-1)^2=1=e^(i*2*pi). It follows that e^(i*2*pi)=e^0. Taking the natural logarithm of both sides: i*2*pi=0, so either i=0, 2=0, or pi=0, all of which are false. Does this make sense? Incredible Question Great Question Good Question • 88 Votes. • 2 Comments • Flag Tanny Libman's comment. 6 years ...