# Complex Numbers resources

### 3GP Mobile Phone (10)

Adding and Subtracting Complex Numbers

This mobile phone video explains how complex numbers can be added or subtracted. There is an accompanying leaflet. Sigma resource Unit 4.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Division of complex numbers

This mobile phone video explains how to divide complex numbers. Sigma resource Unit 7.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Imaginary numbers and quadratic equations

This mobile phone video shows how the imaginary number i can be used in the solution of some quadratic equations. Sigma resource Unit 2.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Motivating the study of complex numbers

This mobile phone download introduces complex numbers by explaining how it is useful to be able to formally write down the square root of a negative number. Sigma resource Unit 1.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Multiplying complex numbers

This mobile phone video explains how complex numbers can be multiplied together. There is an accompanying leaflet. Sigma resource Unit 5.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The Argand Diagram

This mobile phone video explains how complex numbers can be represented pictorially using an Argand Diagram. Sigma resource Unit 8.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The complex conjugate

This mobile phone video explains what is meant by the complex conjugate of a complex number. Sigma resource Unit 6.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The modulus and argument of a complex number

This mobile phone video explains how to calculate the modulus and argument of a complex number. Sigma resource Unit 9.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The polar form of a complex number

This mobile phone video explains what is meant by the polar form of a complex number. Sigma resource Unit 10.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

What is a complex number

This mobile phone video explains what is meant by a complex number, and how to find its real and imaginary parts. Sigma resource Unit 3.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

### Community Project (1)

Integration: Laplace Transforms SOURCE

A zip file containing LaTeX source and eps files for the quick reference leaflet 'Integration: Laplace Transforms' contributed to the mathcentre Community Project by Leslie Fletcher, Liverpool John Moores University

### Guides (1)

Just the Maths (A.J.Hobson)

"Just the Maths" authored by the late Tony Hobson, former Senior
Lecturer in Mathematics of the School of Mathematical and
Information Sciences at Coventry University, is a collection of separate mathematics units, in chronological
topic-order, intended for foundation level and first year
degree level in higher education where mathematics is a service discipline e.g. engineering.

### iPOD Video (9)

Adding and Subtracting Complex Numbers

This mp4 video explains how complex numbers can be added or subtracted.
There is an accompanying leaflet. Sigma resource Unit 4.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Division of complex numbers

This mp4 video explains how to divide complex numbers. Sigma resource Unit 7.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Imaginary numbers and quadratic equations

This mp4 video shows how the imaginary number i can be used in the solution of some quadratic equations. Sigma resource Unit 2.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Motivating the study of complex numbers

This mp4 video introduces complex numbers by explaining how it is useful to be able to formally write down the square root of a negative number. Sigma resource Unit 1.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Multiplying complex numbers

This mp4 video explains how complex numbers can be multiplied together.
There is an accompanying leaflet. Sigma resource Unit 5.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The Argand Diagram

This mp4 video explains how complex numbers can be represented pictorially using an Argand Diagram. Sigma resource Unit 8.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The complex conjugate

This mp4 video explains what is meant by the complex conjugate of a complex number. Sigma resource Unit 6.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The modulus and argument of a complex number

This mp4 video explains how to calculate the modulus and argument of a complex number. Sigma resource Unit 9.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

What is a complex number

This mp4 video explains what is meant by a complex number, and how to find its real and imaginary parts. Sigma resource Unit 3.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

### Quick Reference (18)

Adding and Subtracting Complex Numbers

This leaflet explains how complex numbers can be added or subtracted.
There are accompanying videos. Sigma resource Unit 4.

Complex arithmetic

This leaflet explains how complex numbers can added, subtracted, multiplied and divided. (Engineering Maths First Aid Kit 7.2)

Division of complex numbers

This leaflet explains how to divide complex numbers. Sigma resource Unit 7.
There are accompanying videos.

Imaginary numbers and quadratic equations

This leaflet shows how the imaginary number i can be used in the solution of some quadratic equations. Sigma resource Unit 2.

Integration: Laplace Transforms

Reviews the techniques of integration needed to find and manipulate Laplace Transforms. This Quick Reference leaflet is contributed to the mathcentre Community Project by Leslie Fletcher and reviewed by Martin Randles, Liverpool John Moores University.

Motivating the study of complex numbers

This unit introduces complex numbers by explaining how it is useful to be able to formally write down the square root of a negative number. Sigma resource Unit 1.

Multiplication and division in polar form

This leaflet explains how complex numbers in polar form can be multiplied and divided.
In polar form, these operations are particularly simple to carry out.(Engineering Maths First Aid Kit 7.6)

Multiplying complex numbers

This leaflet explains how complex numbers can be multiplied together.
There are accompanying videos. Sigma resource Unit 5.

The Argand diagram

This leaflet explains how an Argand diagram is used to provide a pictorial representation of a complex number. (Engineering Maths First Aid Kit 7.3)

The Argand Diagram

This leaflet explains how complex numbers can be represented pictorially using an Argand Diagram.
There are accompanying videos. Sigma resource Unit 8.

The complex conjugate

This leaflet explains what is meant by the complex conjugate of a complex number.
There are accompanying videos. Sigma resource Unit 6.

The exponential form

Complex numbers can be written in exponential form. This leaflet explains how this is done. (Engineering Maths First Aid Kit 7.7)

The form r(cos(t) + j sin(t))

This leaflet explains how a complex number
can be written in the form
z=r(cos(t) + j sin(t)). (Engineering Maths First Aid Kit 7.5)

The modulus and argument of a complex number

This leaflet explains how to calculate the modulus and argument of a complex number.
There are accompanying videos. Sigma resource Unit 9.

The polar form

This leaflet explains the polar form of a complex number. It defines the modulus and argument of a complex number. (Engineering Maths First Aid Kit 7.4)

The polar form of a complex number

This leaflet explains what is meant by the polar form of a complex number.
There are accompanying videos. Sigma resource Unit 10.

What is a complex number

This leaflet explains what is meant by a complex number, and how to find its real and imaginary parts. Sigma resource Unit 3.

What is a complex number ?

This leaflet gives a simple, brief introduction to the concept of a complex number. (Engineering Maths First Aid Kit 7.1)

### Test Yourself (9)

Basic complex numbers - Numbas

6 questions on complex numbers, multiplication, inverse, division and modulus. Finding the distance between complex numbers. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Complex Numbers Arithmetic - Numbas

6 questions on complex numbers, multiplication, inverse, division and modulus and finding the distance between complex numbers.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Complex Numbers Test 01 (DEWIS)

Seven questions on complex numbers. Testing modulus, multiplication, division, Argand diagram, polar form, De Moivre's theorem. DEWIS resources have been made available under a Creative Commons licence by Rhys Gwynllyw & Karen Henderson, University of the West of England, Bristol.

Complex Roots of Polynomials - Numbas

2 questions finding roots of real polynomials.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Complex roots of real polynomials - Numbas

Finding roots of a cubic and the roots of a quartic by inspection. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Maths EG

Computer-aided assessment of maths, stats and numeracy from GCSE to undergraduate level 2. These resources have been made available under a Creative Common licence by Martin Greenhow and Abdulrahman Kamavi, Brunel University.

Modulus and argument - Numbas

Find the modulus and argument of complex numbers. One question. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Polar Form and De Moivre's Theorem - Numbas

3 questions. Finding modulus and argument of complex numbers. Use De Moivre's Theorem to find powers of complex numbers. Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Polar form and De Moivre's Theorem - Numbas

3 questions. Finding modulus and argument of complex numbers. Use De Moivre's Theorem to find powers of complex numbers

### Video (10)

Adding and Subtracting Complex Numbers

This video explains how complex numbers can be added or subtracted.
There is an accompanying leaflet. Sigma resource Unit 4.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Division of complex numbers

This video explains how to divide complex numbers. Sigma resource Unit 7.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Imaginary numbers and quadratic equations

This video shows how the imaginary number i can be used in the solution of some quadratic equations. Sigma resource Unit 2.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Motivating the study of complex numbers

This video introduces complex numbers by explaining how it is useful to be able to formally write down the square root of a negative number. Sigma resource Unit 1.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Multiplying complex numbers

This video explains how complex numbers can be multiplied together.
There is an accompanying leaflet. Sigma resource Unit 5.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The Argand Diagram

This video explains how complex numbers can be represented pictorially using an Argand Diagram. Sigma resource Unit 8.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The complex conjugate

This video explains what is meant by the complex conjugate of a complex number.
There is an accompanying leaflet. Sigma resource Unit 6.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The modulus and argument of a complex number

This video explains how to calculate the modulus and argument of a complex number. Sigma resource Unit 9.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The polar form of a complex number

This video explains what is meant by the polar form of a complex number. Sigma resource Unit 10.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

What is a complex number

This video explains what is meant by a complex number, and how to find its real and imaginary parts. Sigma resource Unit 3.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

### Video with captions which require edits (7)

Adding and Subtracting Complex Numbers

This video explains how complex numbers can be added or subtracted.
There is an accompanying leaflet. Sigma resource Unit 4.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Division of complex numbers

This video explains how to divide complex numbers. Sigma resource Unit 7.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Imaginary numbers and quadratic equations

This video shows how the imaginary number i can be used in the solution of some quadratic equations. Sigma resource Unit 2.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Motivating the study of complex numbers

This video introduces complex numbers by explaining how it is useful to be able to formally write down the square root of a negative number. Sigma resource Unit 1.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

Multiplying complex numbers

This video explains how complex numbers can be multiplied together.
There is an accompanying leaflet. Sigma resource Unit 5.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

The complex conjugate

This video explains what is meant by the complex conjugate of a complex number.
There is an accompanying leaflet. Sigma resource Unit 6.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.

What is a complex number

This video explains what is meant by a complex number, and how to find its real and imaginary parts. Sigma resource Unit 3.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.