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The problem with this fraction is the "i" on the denominator, it is not rational. To rationalise this fraction we use the complex conjugate.

This sounds more co...

We can use Pythagoras' Theorem applied to co-ordinates of these points.

A derivative is a mathematical description of how one quantity will change with respect to another. For example the 1st derivative of some function will give you the gradient of the tangent at every point...

Partial fractions are just another technique to simplify expressions to make them easier to manipulate in more complex questions. This is a low mark questions, testing your skills at using partial frac...

First you need to find the vector AB. This is equal to -OA+OB.

OA and OB are equal to the position vectors of A and B respectively so

 -OA+OB=  -2i - 6j + k + 3i + 4j + k = ...