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First of all calculate the complex conjugate of the denominator. The complex conjugate of (1-i) is 1+i.Now multiply the given complex number by (1+i)/(1+i), note that we are not modifying the starting num...

The length of an arc between two points on a curve can be calculated in two ways; as the integral of ((dy/dx)^2 + 1)^1/2 between the values of the points, or as the integral of ((dy/dt)^2+(dx/dt)^2)^1/2 b...

Invert the translation of (2,3) to get the parabola passing through the point (4,7)-(2,3)=(2,4). This is the same as saying that y=4 when x=2, substitute this into your equation y^2=4ax to get a=2.This wi...

Recall that the Maclaurin series for f(x) is f(x) = f(0) + f'(0)x + f''(0)x²/2! + ... + f^(r)(0)x<...

With induction we start with the base case n = 1. So setting n=1 we find that f(1) = 391 which is equal to 17x23. So indeed the base case holds.We assume that for positive integers k, f(k) is divisible by...