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Further Mathematics

A Level

Finding modulus and argument of complex number (x+iy)

Draw argand diagram

Modulus=|z|= length of the line

So |z|=(x²+y²)^0.5

Argument=Angle between real (x axis) and line

so arg(z)=arctan(y/x)

Answered by Emma F. • Further Mathematics tutor

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a) Find the general solution to the differential equation: f(x)=y''-12y'-13y=8. b) Given that when x=0, y=0 and y'=1, find the particular solution to f(x).

First consider y''-12y'-13y=0.

Try: y=e^mx. This gives y'=me^mxand y''=m²e^mx.

Substituting into the differntial equation we get: m²e

Answered by Antonia P. • Further Mathematics tutor

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How do I prove that the differential of coshx is equal to sinhx?

Before this proof, it is important to appreciate that both of these hyperbolic functions can be written in terms of e^x. Therefore, before you begin to differentiate, you must represent coshx as (e^x + e...

Answered by Thomasina R. • Further Mathematics tutor

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Find the root of the complex 3+4i

What we should know is that the root 3+4i is a complex number that looks alot like a+bi.

We can say : rt(3+4i) = a+bi (Where we dont know what a & b is..yet)

and when we square both side...

Answered by Ade A. • Further Mathematics tutor

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Why is the integral of 1/sqrt(1-x^2)dx = sin^{-1}(x)?

This is an example of an integral that uses trigonometric substitutions, which is quite a common theme for A-level further maths questions. Firstly, notice the denominator is quite unpleasant, so to make ...

Answered by Callum B. • Further Mathematics tutor

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