# FP1 crucial points

FP1 crucial points for edexcel

- Created by: Maja
- Created on: 31-05-12 12:47

First 449 words of the document:

Further Pure 1

Crucial Points

Complex numbers

1. Simplify where possible. Remember that when you are working with complex numbers, you should always simplify

i² to -1.

2. Make sure that you know what a complex conjugate is. Remember that for a complex number z = x + iy, the

complex conjugate z* = x iy.

3. Remember that the product of a complex number and its conjugate is real. In particular, when dividing complex

numbers you need to use the fact that zz* is always real.

4. Make sure that you can plot complex numbers correctly on the Argand diagram. Remember in particular that

the points z and z* are reflections of each other in the x axis, and that the points z and z are rotations of each other

through 180° about the origin.

5. Make sure that you know how addition and subtraction of complex numbers is shown in the Argand

diagram, using vectors. You need to understand that a complex number can be represented not only by a point in

the Argand diagram, but alternatively by a vector.

6. Make sure that you know how to find the modulus of a complex number. In particular, don't forget to take the

square root!

7. Make sure that you understand what the modulus represents in the Argand diagram. Remember that |z| is the

distance of the point representing z from the origin, and |z w| is the distance between the points representing z

and w.

8. Be very careful when you find the argument of a complex number. Always decide first which quadrant the

complex number is in. It's a good idea to make a rough sketch of the number on an Argand diagram, so you can `see'

the argument.

E.g.

9. Make sure that you get the sign of the argument right. The argument is measured in an anticlockwise direction

from the positive real axis. Complex numbers below the real axis have negative arguments and those above or on the

real axis have argument greater than or equal to zero.

10. Remember that complex roots of polynomial equations with real coefficients always occur in conjugate

pairs. This is important when solving polynomial equations. If you know one complex root, then you know a second

complex root (its conjugate) and you can then find a quadratic factor with real coefficients for the equation.

11. Make sure that you can divide a polynomial by a linear or quadratic factor.

12. Check your work carefully. It is easy to make mistakes in the algebra when solving polynomial equations.

Matrices

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