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Can anyone prove i to the power i where i is square root of -1 is rational?
Wiki User
∙ 9y ago
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].
Wiki User
∙ 9y ago
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Does there exist an irrational number such that its square root is rational?
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Is 11 squared rational or irrational?
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Is the square root of 6 rational?
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The same reasoning you may have seen in high school to prove that the square root of 2 is not rational can be applied to the square root of any natural number that is not a perfect square.
How you prove that -if r is rational and x is irrational then prove that r x and rx are rational?
You cannot, because the statements are false! (The second is rational only if r = 0).
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It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Math help can anyone show you how to do this please Prove or disprove that if a and b are rational number then ab is rational?
To prove a number ab is rational, you have to find two integers t and n such that t/n = ab.Since we know that a, and b are rational, they can be expressed as follows:a = p1/q1b = p2/q2then ab = p1p2/q1q2Since p1, p2, q1, and q2 are all integers, p1p2 is an integer, and q1q2 is an integer. This gives us the t, and n we are looking for. t = p1p2 and n = q1q2, and ab = t/n, so ab is rational.
How do you prove pi is rational?
pi is irrational so that's impossible
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This is impossible to prove, as the square root of 2 is irrational.
