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It is always helpful to start by drawing a diagram with a Real and Imaginary axis then plotting the number (in our case 1+2i) on the diagram and drawing a line from the origin to our point. Remember the m...

The key fact here is in free fall everything accelerates at the same rate. Acceleration is equal to 9.81 m/s² (accleration of free fall). This means provided you drop both at the same height, a...

We'll need to use the product rule.

Let's take u = x^2 -> du/dx = 2x, and v = ln(x) -> dv/dx = 1/x

Then dy/dx = x^2(1/x) + 2xln(x) = x + 2xln(x)

Substituting our x value gives (...

Socialists tend to support collectivism as they believe that both society and individuals benefit from a cooperative economic system. Socialists argue that humans are best able to fulfil their potential w...

First we differentiate the substitution giving, du/dx=-sinx, which is rearanged to dx=du/-sinx. we can then substitute this into the integral to get sinx e^cosx+1 du/-sinx which can be simplified to -e^co...