Question 3 on Paper 1 covers these two topics, which are apparently unconnected. Not that it concerns us, but the topics become interwoven at university level maths. Anyway this question is one of the more popular on the first paper, and has often been the easiest question on the paper. There have been exceptions; in 1998, Question 3(c) was particularly difficult.
Complex numbers deal with the so-called 'imaginary unit', i, which stands for the square root of -1. It might at first appear as if this quantity has nothing to do with the world we live in, not existing in the way the number 3 'exists'. However, complex numbers have many applications in engineering, physics and science in general. On our course we discuss the properties of complex numbers, see how they help us to solve equations and investigate how to use complex numbers written in polar form.
Matrices were originally introduced to simplify the maths involved in transformation geometry, although in Question 3 on Paper 1 we do not see them being used for this purpose. We concentrate on the definitions associated with matrices and how we can perform the basic operations of addition, multiplication, etc. One interesting feature of matrices is the absence of division, and the use of the inverse of a matrix to overcome this problem.
Topic Structure: Complex Numbers
The study of Senior Cycle Complex Numbers can be divided into the following sections:
1. Definitions and Basic Operations
2. Complex Equations
3. Polar Form of a Complex Number
Topic Structure: Matrices
The study of Senior Cycle Matrices can be divided into the following sections:
1. Properties of Matrices
2. Inverse Matrices and Matrix Equations
This is quite a high-powered site, going very far into the theory of complex numbers. But the first section will be of interest to Leaving Cert students.
The S.O.S. site on matrices is again aimed at students starting university, and so many of the questions refer to matrices of higher dimension than the 2 x 2 that we are used to.
This section covers a wide area of problems about complex numbers, with many well-worked examples provided at three different levels, along with good practice material.
More from the PING site, covering a comprehensive introduction to Matrices.
The complex numbers page from the 'Ask Dr Math' site contains previously asked questions and their answers, many of which are relevant to our course.