How to extend the number system to include and the definition of a complex number.

How to add, subtract, multiply and divide complex numbers.

How to represent complex numbers on an Argand diagram and the modulus and argument of a complex number.

How to write complex numbers in modulus-argument form.

How to define loci in the complex plane.

How to define a matrix by its order.

How to add and subtract conformable matrices.

How to multiply two conformable matrices.

How to use matrices to define linear transformations.

How to find invariant lines and lines of invariant points.

How to find the determinant and inverse of a 2 x 2 and 3 x 3 matrix.

How to use matrices to solve systems of linear equations.

How to use standard series formulae to find the sums of other series.

How to separate algebraic fractions into partial fractions.

How to use the method of differences to find the sum of a series.

How to find the scalar (dot) product of two vectors.

How to define the equation of a line using vectors.

How to define a plane using vectors.

How to use vectors to solve problems involving lines and planes.