8/13/2019 FP1 Revision with obscure parts

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Chapter 1Real numberscomplex conjugate pair are z = a + biand z* =a bi.

Example Find the quadratic equation that has roots 2 + 3iand 23i

( )( )

A complex number can use Cartesian coordinates in an Argand diagram: Additionof complex numbers addition of vectors Modulusthe magnitude of the vector; modulus of given by Argument (arg z)the angle between the positive real axis and the vector representing z on the

Argand diagram. Always , or ! Modulus-argument form- is given by =arg, = I OA I

Ex 1G: Q6, Q9

Roots always come in pairs when dealing with Ex 1H: Q11

Chapter 3Parabola

General point on parabola is , with the equation , Use (p47)Rectangular hyperbola

General point on hyperbola is ,or , with the equation , with asymptotes withequations and

When dealing with simultaneous equations, BEWAREChapter 4 Matrices are not commutative (A.B) doesnt equal (B.A) When multiplied, the number of columns in the LH matrix = number of rows in the RH matrix The product will have the same number of rows as the LH matrix and the same number of columns as the

RH matrix

A linear transformation has the special properties. A linear transformation T has these properties:

1. , where k is a constant

2. [ ] The linear transformation T: can be represented by the matrix With multiple transformations, go from right to left. The determinant is , and the inverse is ( . When the matrix is singular.

Rotation of 2700

means 2700

anticlockwise. Area of Image = Area of object x Idet(M)I REMEMBER Idet(m)I is +ve and ve Simultaneous equations p104Chapter 5