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Say we want to find a value for x which makes this equal to i, so want cos(x) = 0 and sin(x) = 1. x = pi/2 is a value which satisfies this. So e^(i*pi/2) = i. So now that we have this seemingly more complicated way of writing i, we can substitute it for the base of our exponent and raise it to the power of i. So we get (e^(i*pi/2))^i.
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Consider the function f(x) = x+ 1/x, x belongs to R, x is not equal to 0 Is f Maths
Algebra Simplify (x-i) (x+i) (x − i) (x + i) ( x - i) ( x + i) Expand (x−i)(x+i) ( x - i) ( x + i) using the FOIL Method. Tap for more steps. x⋅x+xi− ix−ii x ⋅ x + x i - i x - i i Simplify terms. Tap for more steps. x2 + 1 x 2 + 1
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Limit of (1+1/x)^x as x approaches ∞
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t. e. Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has. where e is the base of the natural logarithm, i is the imaginary.
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Roman numeral, any of the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, standing respectively for 1, 5, 10, 50, 100, 500, and 1,000 in the Hindu-Arabic numeral system.
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2 Answers Sorted by: 9 For any r.v. X X I(X, X) = H(X). I ( X, X) = H ( X). To see this, put Y = X Y = X in I(X, Y) = H(X) − H(X|Y) I ( X, Y) = H ( X) − H ( X | Y) and use H(X|X) = 0. (∗) H ( X | X) = 0. ( ∗)
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Ex 7.5, 23 (MCQ) Integrate dx / x (x^2 + 1) equals (A) log x 1/2
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