Let the fantastic wealth of resources below teach you all about Argand Diagrams ...

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Resources used with students in Scottish Secondary Schools

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A sound understanding of Argand Diagrams is essential to ensure exam success.

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Please find below:

3. MIA Text Book Questions – Complex Numbers

5. AH Maths Past & Practice Papers

6. AH Maths Past Paper Questions by Topic

7. AH Maths Recommended Text Book

8. Exam Focused Online Study Pack – *For students looking for a ‘good’ Pass*

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**1. Links and Exam Formulae
**

AH Maths - Home Page Link | HERE |

AH Maths - Whole Course Link | HERE |

AH Maths - Exam Formula List | HERE |

Higher Maths - Exam Formulae List | HERE |

AH Maths - Complete Formula List | HERE |

SQA Full Course Content and Outline | HERE |

**2. Complex Numbers Resources**

Thanks to the author(s) for making these available.

Complex Numbers Theory Guide 1 | HERE |

Complex Numbers Theory Guide 2 | HERE |

Complex Numbers Theory Guide (HSN) | HERE |

**3. MIA Text Book Questions – Complex Numbers**

Recommended questions from the new MIA Text Book are shown below.

Worked solutions to all questions below are available in the Online Study Pack.

Subtopic _________________________________ | Page Number _____________ | Exercise ___________ | Questions _________________________ | Worked Solutions _______________ |

Arithmetic with Complex Numbers | Page 207 | Exercise 12.1 | Q1,2,3,6,7,8 | HERE |

Division & Square Roots of Complex Nos | Page 209 | Exercise 12.2 | Q1a,b,c,2c,e,3a,b,f,5a,b | HERE |

Argand Diagrams | Page 211 | Exercise 12.3 | Q3a,b,d,e,f,i,6a,b,f,7a,b,c | HERE |

Multiplying/Dividing in Polar Form | Page 215 | Exercise 12.5 | Q1a,b,f,g | HERE |

De Moivre's Theorem | Page 218 | Exercise 12.6 | Q1,2,3a,4g,h,i,j | HERE |

Polynomials & Complex Numbers | Page 224 | Exercise 12.8 | Q2a,d,3a,b,4,5,6a,b | HERE |

Loci on the Complex Plane | Page 213 | Exercise 12.4 | Q1a,b,d,f,j,3a,b,4a,b,c | HERE |

Expanding Trig Formula | Page 219 | Exercise 12.6 | Q5,6,7a | HERE |

Roots of a Complex Number | Page 222 | Exercise 12.7 | Q2a,b,c,d,e,f,1a(i) | HERE |

**4. About Argand Diagrams
**

For a more detailed explanation, please first read the Theory Guides above.

The Argand Diagram is a geometric way of representing complex numbers.

In the above, if z is a point on the line with coordinates (a,b) then the diagram shows a general complex number:

z = a + bi

The distance z from the origin is called the **modulus** of z, denoted by **|z|**

If z = a + bi then

|z| = + √(a² + b²)

The angle (in radians), ∅, that the line from the origin to z makes with the positive x-axis is called the **argument** of z, denoted by **arg z. **

The angle is written as between – 180º ≤ ∅ ≤ + 180º

If z = a + bi then

- arg z = inverse tan (b/a) where a ≠ 0
- arg z = ∅ + 2nΠ where n = integer

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**Exam Question**

**Source: SQA AH Maths Paper 2014 Question 16**

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**5. AH Maths Past & Practice Papers**

Thanks to the SQA for making these available.

Worked solutions to SQA Exam Questions available in the Online Study Pack.

Year _____ | Paper Type _________________ | Exam Paper ______________ | Marking Scheme _________________ |

2018 | Advanced Higher | Exam Paper | Marking Scheme |

2017 | Advanced Higher | Exam Paper | Marking Scheme |

2016 | Advanced Higher | Exam Paper | Marking Scheme |

2016 | AH Specimen | Specimen | |

2016 | AH Exemplar | Exemplar | Exemplar Guidance |

2015 | Advanced Higher | Exam Paper | Marking Scheme |

2014 | Advanced Higher | Exam Paper | Marking Scheme |

2013 | Advanced Higher | Exam Paper | Marking Scheme |

2012 | Advanced Higher | Exam Paper | Marking Scheme |

2011 | Advanced Higher | Exam Paper | Marking Scheme |

2010 | Advanced Higher | Exam Paper | Marking Scheme |

2009 | Advanced Higher | Exam Paper | Marking Scheme |

2008 | Advanced Higher | Exam Paper | Marking Scheme |

2007 | Advanced Higher | Exam Paper | Marking Scheme |

2006 | Advanced Higher | Exam Paper | Marking Scheme |

2005 | Advanced Higher | Exam Paper | Marking Scheme |

2004 | Advanced Higher | Exam Paper | Marking Scheme |

2003 | Advanced Higher | Exam Paper | Marking Scheme |

2002 | Advanced Higher | Exam Paper | Marking Scheme |

2001 | Advanced Higher | Exam Paper |

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**6. AH Maths Past Paper Questions by Topic**

Thanks to the SQA for making these available.

Questions and answers have been split up by topic for ease of reference.

Worked solutions to all SQA questions below available in the Online Study Pack.

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**7. ****AH Maths Text Book – Maths In Action (2nd Edition) by Edward Mullan **

A fully revised course for the new Curriculum for Excellence examination that is designed to fully support the course’s new structure and unit assessment. A part of the highly regarded Maths in Action series, it provides students with a familiar, clear and carefully structured learning experience that encourages them to build confidence and understanding.

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**8. Exam focused Online Study Pack
**

Through step-by-step worked solutions to exam questions available in the Online Study Pack we cover everything you need to know about Argand Diagrams and Complex Numbers to pass your final exam.

As well as students studying Advanced Higher Mathematics, the resources will benefit young adults studying A-Level Mathematics and undergraduates who need a little extra help. Particular benefit will be to students who have gained a ‘Conditional’ University place and are therefore required to pass in order to gain entry onto the course of their choice.

Subscribing to the Online Study Pack may therefore be one of your best ever investments. Please click Online Study Pack to view screenshots, examples and instructions on how to subscribe.

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We hope the resources on this website prove useful and wish you the very best of success with your AH Maths course in 2018/19.

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Topic Links

Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right