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

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.

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Author(s): The Open University

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

Ahmed, A. (1987) Better Mathematics, London, HMSO.
DfEE (2001) Key Stage 3 National Strategy: Framework for Teaching Mathematics: Years 7, 8 and 9, London, DfEE.
NCTM (1989) Curriculum and Evaluation Standards for School Mathematics Reston VA, National Council of Teachers of Mathematics.

Author(s): The Open University

In this course you have been introduced to the difference between mathematical content and processes. You have worked on the do–talk–record (DTR) framework for learning mathematics.

Author(s): The Open University

The third configuration of air column that we shall consider is that enclosed by a conical tube. Figure 17 shows the normal modes of vibration for a conical tube plotted in terms of pressure. As you would expect, there is a pressure antinode at the closed tip of the cone and a pressure node at the open en
Author(s): The Open University

We'll now turn our attention to the setting up of standing waves in an air column contained within a cylindrical tube that is open at one end but closed at the other. Straight away we can say that the closed end must be a displacement node since the air molecules can't move at this boundary. That means it must be a pressure antinode. The open end, as we saw previously, will be a displacement antinode (that is, a pressure node).

Now, you may recall that the distance between a node and a
Author(s): The Open University

Perceptions of English literature
To what extent has the definition of English literature changed over the last 50 years? What criteria do we use when classifying a novel as English? And is this definition organic enough to assimilate new works and different interpretations? Professor Terry Eagleton leads the discussion by explaining how perceptions of Englishness changed during the 20th century and we discover that as a result of authors such as Chinua Achebe, Andrea Levy and Marina Levitska, notions of what was an English nove
Author(s): The OpenLearn team

Think of it like this: each genre novel suggests certain characteristics, qualities and plot patterns that are particular to that genre. When you read a murder-mystery, you expect there at least to be a murder, or some kind of love interest in a romance. The reader has certain expectations. To fulfil them – the murder-mystery opening with a dead body; the romance delivering the passions of a hero and heroine – means that readers recognise the familiar elements and progressions of the stor
Author(s): The Open University

Goya developed from a decorator of churches to a court artist, accomplished portraitist, satirical graphic artist and a painter of dark, nightmare visions. His work at court, for Carlos III and Carlos IV, involved both decorative work and a series of portraits of key figures who moved in court circles. As his official, public work became more sought after, however, he developed a parallel career as a graphic artist that seemed to express more freely a private view of the injustices, vices, fo
Author(s): The Open University

Image 9 Phot
Author(s): The Open University

Having asked you to think about these perspectives on religion and approaches to its study, I must again emphasize that this is a very crude way of characterizing a very complex area of research. These perspectives are not watertight compartments into which all study of religion fits – life is not that simple! Some religious standpoints are themselves reductionist: for example, Anglicans in the ‘Sea of Faith ’movement regard themselves as Christians, while considering belief in the supe
Author(s): The Open University

The purpose of studying religion is to make the strange familiar, and the familiar strange.

### Exercise

We would encourage
Author(s): The Open University

Some themes recur when we start to think about religion. These include issues of continuity and change, representation, differing perspectives, authority, community and identity. In this course we start to consider some of them in detail.

The full list of themes and issues considered in this section are:

• Continuity and change

• Representation

• The Victoria and Albert Museum 'Sacred Spaces' exhibition of 2000

• Author(s): The Open University

The previous section introduced you to a music tradition which places great demands on the inventiveness and virtuosity of a single individual. Although this individual is supported by accompanists, it is to a large extent a soloistic music. We will now move on to a very different kind of music, in a tradition which places more emphasis on group interaction and ensemble playing. This is gamelan music of Sunda, an area comprising roughly the western third of the island of Java, in Indon
Author(s): The Open University

How do financial markets match providers with users, and how efficiently does the market determine prices? Financial markets can be notoriously volatile, and the stock market is possibly the most volatile of them all. This is after all the place where, depending on skill or on luck, investors either ‘make a killing’ or ‘lose their shirts’. But which does it depend on – skill or luck? Or does it depend on a mixture of the two? In this unit, you will find the answers to these key que
Author(s): The Open University

Allow 60 minutes for this activity.

You have spent most of this course working with Hofstede's ideas. He is one of the pioneers of the study of national culture and its impact on organisations, and his work has been very influential.

My aim so far has been to help you understand Hofstede's cultural dimensions and to become familiar with how they can be used to analyse one of the main environments within which organisations operate. National culture is also one of the factor
Author(s): The Open University

Allow 60 minutes for this activity.

In the last few activities you have been exploring Hofstede's ideas. I now want to focus specifically on an issue which has already cropped up a couple of times. This is the impact that national culture has on organisations. One of Hofstede's main arguments is that it is important for business organisations to adapt their approaches to different national contexts.

Take the example of shopping. Income is an important influence on the thing
Author(s): The Open University

Globalisation is something we tend to take for granted, mostly in the form of the remarkably low prices we pay for our consumer goods. When the first pocket calculator was launched in the UK in 1972, it cost £79 plus tax, an amount close to the average monthly take home pay.

Ten years later came the original IBM PC. Replete with a 4.77 MHz processor, 64kB RAM, a 12″ monochrome monitor (and an optional floppy disk drive!), it carried a UK price tag in excess of £1500, at that time a
Author(s): The Open University

The reservation wage is one of many meeting points between personal lives and social policies. Personal lives fundamentally condition the rate of pay at which everyone individually decides they can or must work. Policies like New Deal necessarily regulate that level.

## Activity 5

Author(s): The Open University