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1.2 Audio files

The following files accompany the exercise in Section 4.2

Clicking on 'View document' below opens an extract from Section 4.2 of the unit (PDF, 1.7 MB) which accompanies the audio clips, also below. Listen to each of them in turn with the extracted pages open (you may like to print them out). Work on the problems at the appropriate places – you'll find the answers at the foot of this page.

Learning outcomes

After studying this unit 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

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Introduction

This unit is an adapted extract from the Open University course Complex analysis (M337)

This unit is devoted solely to complex numbers.

In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.

Section 2 is devoted to the geometric representation of complex numbers. You will find that
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1.6.4 Blogs

Technorati reports that over 100 000 new ‘blogs’ are created each day. Because these online diaries offer instant publishing opportunities, you potentially have access to a wealth of knowledge from commentators and experts (if they blog) in a wide range of fields. Most internet searches will turn up results from blogs, but there are some blog-specific search engines such as: Blogdigger
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1.6.2 Alerts

Online bookshops and some of the major search engines offer ‘Alerts’ services. These work by allowing you to set up a profile once you have registered on their site, and when there are items meeting your criteria you receive an email. The good thing about alerts is that you don’t have to do anything once you have set up your profile. The downside, particularly with alerts services from the search engines, is that given the extent to which internet traffic is on the increase whether new
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1.5.6 Copyright – what you need to know

An original piece of work, whether it is text, music, pictures, sound recordings, web pages, etc., is protected by copyright law and may often have an accompanying symbol (©) and/or legal statement. In the UK it is the Copyright, Designs and Patents Act 1988 which regulates this.

In most circumstances, works protected by copyright can be used in whole or in part only with the permission of the owner. In some cases this permission results in a fee.

However, the UK legislation incl
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1.5.3 Desktop search tools

Finding your paperwork or electronic files can be a problem. You may find that even if you do have some sort of filing system, your structure soon gets quite large with files in multiple locations, which can be hard to navigate. You may find yourself making arbitrary decisions about which folder to place a document in. It may make sense now but in the future, when you look where you think it should be, it’s not there.

At times like this you may resort to the search command from the Wi
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1.4.7 T is for Timeliness

The date when information was produced or published can be an important aspect of quality. This is not quite as simple as saying that 'good' information has to be up to date.

Activity

Here is an example of a news item from an onl
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1.3.9 Summary

There is a lot of information available on maths and statistics via the internet. Try the activities below to start exploring what is available.

Activity

1.3.6 Encyclopedias

Encyclopedias can be useful reference texts to use to start your research. There are some available online, such as Wikipedia, which is a freely available collaborative encyclopedia.


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1.3.5 Journals

Journals and articles written by academics or experts are an excellent source of information. Journals are usually published monthly or quarterly, and contain a selection of articles providing details of recent research. Often they will also contain reviews of relevant books. They are usually published more quickly than books, and so are often more up to date.

To access content of journals, most publishers require a subscription. There are, however, some journals which you can freely ac
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1.3.4 Databases

At a basic level, a database is a collection of information which can be searched. It is a way of storing, indexing, organising and retrieving information. You may have created one yourself to keep track of your references – or your friends' names and addresses. They are useful for finding articles on a topic, and can be used to search for many different types of information.

You may find some of the following databases useful for your topic. They contain different types of informatio
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1.3.3 Books and electronic books

Books are a good source of information. The publishing process (where a book is checked by an editor before publishing, and often reviewed by another author) means that books are reliable sources of information, although they may need to be evaluated for bias. A growing number of books can be found online.

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1.3.2 Search engines and subject gateways

Although both search engines and subject gateways will help you find the resources that you need, the types of information that you find will differ.

Search engines such as Google and Yahoo! search the internet for keywords or phrases, and then show you the results. These results are not mediated by the search engines, and therefore you need to use your own judgement on the reliability of the results. You may, for example, find websites written by experts, alongside websites written by
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1.3.1 Introduction

You can find a lot of information about the maths and statistics on the internet.

To find this information you might choose to use:

  • search engines and subject gateways;

  • books and electronic books;

  • databases;

  • journals;

  • encyclopedias

  • internet resources


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1.2.4 Checklist of common features

  • Is there any online help?

  • Can I do a simple search?

  • Can I look at the information in both short and detailed form?

  • Can I choose where in the record I want my search terms to be found?

  • Can I search for phrases?

  • Can I combine search terms?

  • Can I use truncation?

  • Can I use wildcards?

  • Can I do an advanced search?

  • <
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1.2.3 Basic principles

Whatever resource you choose to use to find information on the internet, many of the same principles apply. Each source that you use will probably look quite different from the one you tried before, but you'll notice that there are always features that are similar – a box to type your search terms in, for instance, or a clickable help button. Different resources refer to the same functions using different terminology, but the principles behind them are exactly the same. The trick is to chec
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1.2.1 Planning your search

Your approach to searching will depend to a great extent on what kind of person you are. In an ideal world, when searching for information for a specific purpose, we would all find what exactly we were looking for at the first attempt, especially if we are in a hurry. However, it’s always a good idea to have some kind of plan when you are searching for information, if only to help you plan your time and make sure you find the information you need. If I was starting to search for material on
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1.1.6 Keeping up-to-date

How familiar are you with the following different ways of keeping up to date with information; alerts, mailing lists, newsgroups, blogs, RSS, professional bodies and societies?

  • 5 – Very familiar

  • 4 – Familiar

  • 3 – Fairly familiar

  • 2 – Not very familiar

  • 1 – Not familiar at all


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1.1.3 Searching for information on maths and statistics

How well does the following statement match what you do when you begin a new search for information?

Before I begin a new search for information (maybe for an assignment, or to help you choose your next holiday destination), I spend some time thinking about what I already know, what the gaps in my knowledge are, and the best types of information to meet my needs.

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