This Argand diagram shows how complex numbers a and b are subtracted to produce the complex number c. This addition is similar to the "parallelogram law" for adding vectors.

the Argand diagram illustrates a - b = c

if a = c + di and b = e + fi, then c = a - b = (c-e) + (d-f)i

|a - b| is not equal to |a| - |b|

the Argand diagram illustrates a - b = c

if a = c + di and b = e + fi, then c = a - b = (c-e) + (d-f)i

|a - b| is not equal to |a| - |b|

## Software/Applets used on this page

Uses Cinderella interactive geometry

## Glossary

### argand diagram

A geometrical presentation of a complex number; using a real and imaginary axis to plot a+ib as (a,b).

### complex number

A number of the form a+bi where i is the square root of -1, and a and b are real.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | FP2 | Complex Numbers | Argand diagram | - |

AQA AS Further Maths 2017 | Pure Maths | Complex Number Basics | Argand Diagrams | - |

AQA AS/A2 Further Maths 2017 | Pure Maths | Complex Number Basics | Argand Diagrams | - |

CBSE XI (India) | Algebra | Complex Numbers and Quadratic Equations | Argand diagrams | - |

CCEA A-Level (NI) | FP1 | Complex Numbers | Argand diagram | - |

CIE A-Level (UK) | P3 | Complex Numbers | Argand diagram | - |

Edexcel A-Level (UK - Pre-2017) | FP1 | Complex Numbers | Argand diagram | - |

Edexcel AS Further Maths 2017 | Core Pure Maths | Argand Diagrams | Argand Diagrams | - |

Edexcel AS/A2 Further Maths 2017 | Core Pure Maths | Argand Diagrams | Argand Diagrams | - |

I.B. Higher Level | 1 | Complex Numbers | Argand diagram | - |

Methods (UK) | M3 | Complex Numbers | Argand diagram | - |

OCR A-Level (UK - Pre-2017) | FP1 | Complex Numbers | Argand diagram | - |

OCR AS Further Maths 2017 | Pure Core | Argand Diagrams and Loci | Argand Diagrams | - |

OCR MEI AS Further Maths 2017 | Core Pure A | Argand Diagrams and Loci | Argand Diagrams | - |

OCR-MEI A-Level (UK - Pre-2017) | FP1 | Complex Numbers | Argand diagram | - |

Pre-U A-Level (UK) | 7 | Complex Numbers | Argand diagram | - |

Scottish Advanced Highers | M2 | Complex Numbers | Argand diagram | - |

Scottish (Highers + Advanced) | AM2 | Complex Numbers | Argand diagram | - |

Universal (all site questions) | C | Complex Numbers | Argand diagram | - |

WJEC A-Level (Wales) | FP1 | Complex Numbers | Argand diagram | - |