# Further Pure 1 FP1 Complete Revision Notes AQA

- Created by: Thomas Fenton
- Created on: 23-04-13 19:21

First 317 words of the document:

FP1 Key Notes

Chapter 1 Complex Numbers

i2 = -1

When adding/subtracting imaginary numbers, just add/subtract real

and imaginary parts

i.e. (4+3i) + (7+8i) = 11+11i

(17+2i) (9+8i) = 8-6i

The complex conjugate of a+bi is a-bi. You multiply an imaginary

number by its complex conjugate pair to rationalise the denominator.

The complex conjugate of z is z*

If the roots of a quadratic equation are complex, and will always be a

complex conjugate pair;

In the form: (x )(x )

Imaginary numbers can be expressed as points on a Cartesian graph on

an Argand Diagram.

The modulus of a complex number z = x + iy is given by x2 + y2

The argument of a complex number is the angle between the positive

real axis and the vector representing z on the Argand diagram

(SohCahToa). The argument is always -180 x 180.

The modulus-argument form of a complex number z = x + iy is given as

Z = modulus x (cos(arg) + i sin(arg))

You can compare real and imaginary parts of an equations to find a and b

e.g. 3+5i = (a+ib)(1+i)

= (a-b) + i(a+b)

i) ab = 3

ii) a+b = 5 so... a=4 and b=1

To find the Square roots of a complex number, make the complex

number equal to (a+bi)2 and solve to find a and b (answer given as

complex num)

For a cubic equation, either all three roots are real or one root is real

and the other two roots form a complex conjugate pair. Use the formula:

X3 ( + )x +

To find unknowns in a cubic, if a root is given, use the other complex

conjugate and form a quadratic then use the grid method

Tom Fenton

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