Before embarking on this course, it is important to take some time to think about the implications of its title: Company law in context. In particular, what constitutes ‘company law’, and what is the context in which we are thinking about it?

At this point, you might like to pause for a moment and contemplate what this phrase means to you. In particular, what do you understand by the concept of a ‘company’?

At first, this may seem like a ludicrously straightforward questio
Author(s): The Open University

After studying this course, you should be able to:

• understand the historical growth of the idea of human rights

• demonstrate an awareness of the international context of human rights

• demonstrate an awareness of the position of human rights in the UK prior to 1998

• understand the importance of the Human Rights Act 1998

• analyse and evaluate concepts and ideas.

Author(s): The Open University

Working mathematically
This free course, Working mathematically, is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process. First published
Author(s): Creator not set

A quadrilateral is a shape with four straight sides.
Author(s): The Open University

## SAQ 26

Find the distance between the numbers 2 − i and 1 + 3i.

Author(s): The Open University

You will no doubt recall that in real analysis extensive use is made of the modulus function . It gives us a way of measuring the “closeness” of two numbers, which we exploit in writing expressi
Author(s): The Open University

We have seen in SAQ 18 of Section 3.4 how some sets of points of the complex plane can be described algebraically in terms of operations on C. We now use the modulus function to take this a step further by defining discs in the complex plane. As we shall see, discs are extensively used in arguments involving l
Author(s): The Open University

## SAQ 13

Find |z| and Arg z in each of the following cases.

1. Author(s): The Open University

We have seen in Section 2.2 that the complex number system is obtained by defining arithmetic operations on the set R × R. We also know that elements of R × R can be represented as points in a plane. It seems reasonable to ask what insight can be obtained by representing complex numbers as
Author(s): The Open University

In this section we have seen that the complex number system is the set R × R together with the operations + and × defined by

From this, one can justify the performance of ordinary algebraic operations on expressions of the form
Author(s): The Open University

You have almost certainly met complex numbers before, but you may well not have had much experience in manipulating them. In this course we provide you with an opportunity to gain confidence in working with complex numbers by working through a number of suitable problems.

Perhaps the most striking difference between real numbers and complex numbers is the fact that complex numbers have a two-dimensional character, arising from our definition of a complex number as an ordered pair of
Author(s): The Open University

Learning outcomes

After studying this course, you should be able to:

• perform basic algebraic manipulation with complex numbers

• understand the geometric interpretation of complex numbers

• know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.

Author(s): The Open University

Acknowledgements

These extracts are from M208 © 2006 The Open University.

All material contained within this course originated at The Open University.

Course image: Matt in Flickr made available under Creative Commons Attribution 2.0 Licence.

Don't miss out:

Author(s): The Open University

Keep on learning

## Study another free course

There are more than 800 courses on OpenLearn for you to
Author(s): The Open University

Conclusion

This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.

Author(s): The Open University

5 Hyperbolic functions

In Section 4 we introduce the hyperbolic functions sinh, cosh and tanh, which are constructed from exponential functions. These hyperbolic functions share some of the properties of the trigonometric functions but, as you will see, their graphs are very different.

Click the link below to open Section 4 (5 pages, 104KB).

Section 4
Author(s): The Open University

1 Overview

A fundamental concept in mathematics is that of a function.

Consider, for example, the function f defined by

This is an example of a real function, because it associates with a given real number
Author(s): The Open University

Keep on learning

## Study another free course

There are more than 800 courses on OpenLearn for you t
Author(s): The Open University

3.4 Decreasing by a percentage

Discount can be calculated in the same way as an increase by a percentage. For example, £8 with 15% discount means you actually pay

£8 less (15% of £8)

15% of 8 = × 8 =
Author(s): The Open University

3.2.1 Try some yourself

## Activity 20

Convert each of the following to percentages. Round off the percentages to whole numbers.

• (a)

• (i) 0.8

• (ii) 0.
Author(s): The Open University