# FP1 Revision Sheet

Basics of all Edexcel FP1 topics.

- Created by: Egg
- Created on: 24-11-11 09:40

First 269 words of the document:

Ellie Griffiths FP1 Revision Sheet

Complex numbers:

Complex numbers are in the form a + bi, where a

and b are real numbers:

The complex conjugate of complex number z:

If roots and of a quadratic are complex, they

will be a complex conjugate pair.

If one root of anything is complex, another root

will be its complex conjugate.

Complex numbers in the form z = x + yi may be

represented on an Argand diagram where (x, y)

are Cartesian coordinates.

The modulus of complex number z = x + yi, known

as r or |z| or |x + yi|:

The argument arg z is the angle between the

positive real (x-) axis and the vector

The modulus-argument form of z = x + yi:

For complex numbers z1 and z2:

Interval bisection:

Find an interval in which f(x) changes sign.

Take the mid-point as an approximation.

Repeat using mid-point between previous mid-point and original limit where there is a change of

sign.

Linear interpolation:

Draw a sketch of function f(x) for given interval [a, b]

Join a line between points on curve at x-coordinates a and b. Where this line intercepts the x-axis is

your next approximation.

Use similar triangles to find this point: ratio of heights is same to ratio of bases.

Repeat using approximation and one of the original limits where there is a change of sign between

them. Repeat until answer found to required degree of accuracy.

Netwon-Raphson:

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