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What does ei pi yo mean?

Updated: 4/28/2022
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14y ago

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: ; Euler's identity http://en.wikipedia.org/wiki/Leonhard_Euler

some pretty hardcore math, but is important in alot of different ways.

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How do you manually calculate i raised to the power of i?

by euler: i=ei(pi)/2 therifore ii = (ei(pi)/2)i=ei^2(pi)/2=e-(pi)/2 ~0.208


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Euler's formula states that: eix = cos(x) + i*sin(x); where "i" is an imaginary number and "x" is an angle value. Under this reasoning, ei*2(pi) equals 1: ei*2(pi) = cos(2(pi)) + i*sin(2(pi)); ei*2(pi) = 1 + i*(0); ei*2(pi) = 1 + 0; ei*2(pi) = 1. Another contributor: Equivalently, e2i*pi - 1 = 0 That statement brings together, in such simplicity, two of the most important transcendental numbers (e and pi), the basic element of complex mathematics (i) and the two identities of arithmetical operations: addition (0), and multiplication (1).


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Can anyone prove i to the power i where i is square root of -1 is rational?

Nobody can prove it because it is not true. It is a real number, though. eix = cos(x) + i*sin(x) Therefore ei*pi/2 = cos(pi/2) + i*sin(pi/2) = 0 + i*1 = i Raising both sides to the ith power, (ei*pi/2)i = ii So that ii = ei*i*pi/2 = e-pi/2 = 0.2079. Gelfond proved that the above value is irrational [transcendental, actually].


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Ei. Pronounced EYE