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E to the pi i equals negative one because of a string of properties. Namely logarithmic properties. When you take the natural log of both sides you are able to bring the exponent of pi and i down. And replace the ln of e with 1. When you keep the natural log of negative 1 you get 3.145....i or pi times i. To understand this natural log place you must go back to the original equation E^pi i. When you take the i root of both sides you get e to the pi alone, and have the i root of negative one. By doing this you are just raising negative 1 to the inverse of i, negative i. When you do this you end up with 23.14069263....... because of derivatives. Guess what e to the pi is. you guessed right 23.14069263. This is commonly known as Eulers's identity. If you want the more in depth understanding Google it, or bing whatever you prefer.
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Is e to the pi rational?
e^pi ~ 23.14069.............., not rational
Is pi divided by e rational?
A rational number is able to be represented as a ratio of polynomials. pi/e is a ratio of irrational numbers, neither of which can be represented as a ratio of polynomials, and so I would conclude that pi/e is not rational. But it's a good question, because what if two irrational numbers could cancel out their irrationality, like two negative numbers! A quotient of two irrational numbers can be a rational number. Trivial example 2pi/pi = 2.
How do you change 7 pie radians into degrees?
The formula for converting radians to degrees is the given angle in radians multiplied by (180 degrees / pi), so in this case, 7 pi radians would be equal to 1260 degrees. (By the way, the greek letter pi isn't spelled with an e).
Why is Euler's formula important?
Euler's formula is important because it relates famous constants, such as pi, zero, Euler's number 'e', and an imaginary number 'i' in one equation. The formula is (e raised to the i times pi) plus 1 equals 0.
What is the area of the inverse circle?
sqr(e/pi)
What is e to the pi i?
negative one.
What is a negative and a positive equal?
A negative e. i. 4X-6=-24
What does e raised to the i times pi equal?
-1. This is a result of Euler's formula.
Is a power a whole number?
Not necessarily. i times pi is not a whole number, and yet e to the power of i times pi is equal to -1.
Pi is equal to 3.14 then what is mc2 equal to?
E=mc2 =0.111x 300,000,000x 300,000,000= 10,000,000,000,000,000 (10 quadrillon) joules.
What is e plus pi plus pi plus pi plus e plus e plus e?
About 20.29791
Is e to the pi rational?
e^pi ~ 23.14069.............., not rational
How can you make rational of i power i?
It is NOT rational, but it IS real.Start with Euler's formula: e^ix = cos(x) + i*sin(x) for all x.When x = pi/2,e^(i*pi/2) = cos(pi/2) + i*sin(pi/2) = 0 + i*1 = ior i = e^(i*pi/2)Raising both sides to the power i givesi^i = e^[i*(i*pi/2)] = e^[i*i*pi/2]and since i*i = -1,i^i = e^(-pi/2) = 0.20788, approx.
How do you manually calculate i to the power of i?
i (taken to be sqrt(-1) for this question) requires that you know a bit about writing complex numbers. i = e^(i*pi/2) so i^i = (e^(i*pi/2))^i which equals e^(i*i*pi/2) since i*i = -1 we get e^(-pi/2) so i^i = e^(-pi/2) which is roughly .207879576
Does transcendental ean it is equal to the ratio of two integers in math?
Absolutely not. Transcendental numbers are such values as e, pi, and root 2
Does a positive integer multiplied by a negative integer equal a negative integer?
All negative integers, when multiplied by a positive integer, or vice versa, will result in a negative integer. I. E. 5*-5=-25
Is pi divided by e rational?
A rational number is able to be represented as a ratio of polynomials. pi/e is a ratio of irrational numbers, neither of which can be represented as a ratio of polynomials, and so I would conclude that pi/e is not rational. But it's a good question, because what if two irrational numbers could cancel out their irrationality, like two negative numbers! A quotient of two irrational numbers can be a rational number. Trivial example 2pi/pi = 2.
