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e^pi ~ 23.14069.............., not rational

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โˆ™ 2010-11-26 04:21:41
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Q: Is e to the pi rational?
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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.

Why rational numbers require extension?

Because numbers such as pi, e and the square root of 2 are 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.

Why is pi rational?

Pi is not rational it is irrational because it does not stop or repeat

Is 3.14 a rational or irrational number?

3.14 is a rational number pi is not. pi is not 3.14

Is 0.16 pie a rational number?

(pi) itself is an irrational number. The only multiples of it that can be rational are (pi) x (a rational number/pi) .

Is 0.0125 rational?

Yes. All rational numbers must terminate or repeat. Rational: 1/3, 1/8, 13, 0.6666666666666... Not rational: π (pi), e, √2

Is 0.3 pi rational?

No, it is not.

Why is pi a rational number?

Pi is irrational.

Can you subtract 2 irrational numbers to get a rational number?

Yes. Example: pi - pi = 0.You can even subtract two different irrational numbers to get a rational number.For example: e - (e - 1) = 1 or Φ - (1/Φ) = 1.

Is 10 pi rational?

No 10*pi is not a rational number because it can't be expressed as a fraction

Is -22 rational?

No 22*pi is not a rational number

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