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This Argand diagram shows how complex numbers a and b are added 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|
Please enable Java for an interactive construction (with Cinderella).


MathsNet imageAn Argand diagram is a plot of complex numbers, z=x+iy, as points in the complex plane using the x-axis as the real axis and y-axis as the imaginary axis.
While Jean-Robert Argand (1768 - 1822) is generally credited with the discovery in 1806, the Argand diagram (also known as the Argand plane) was actually described by C. Wessel prior to Argand. Historically, the geometric representation of a complex number as a point in the plane was important because it made the whole idea of a complex number more acceptable. In particular, this visualization helped "imaginary" and "complex" numbers become accepted in mainstream mathematics as a natural extension to negative numbers along the real line.

Software/Applets used on this page

Uses Cinderella interactive geometry


argand diagram

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


One of two straight lines on a graph from which measurements are taken. One axis (the y axis) is vertical; the other (the x axis) is horizontal.

complex number

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


A sequence where each term is obtained by multiplying the previous one by a constant.


To mark a point on a graph accurately by using its coordinates.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)FP2Complex NumbersArgand diagram-
AQA AS Further Maths 2017Pure MathsComplex Number BasicsArgand Diagrams-
AQA AS/A2 Further Maths 2017Pure MathsComplex Number BasicsArgand Diagrams-
CBSE XI (India)AlgebraComplex Numbers and Quadratic EquationsArgand diagrams-
CCEA A-Level (NI)FP1Complex NumbersArgand diagram-
CIE A-Level (UK)P3Complex NumbersArgand diagram-
Edexcel A-Level (UK - Pre-2017)FP1Complex NumbersArgand diagram-
Edexcel AS Further Maths 2017Core Pure MathsArgand DiagramsArgand Diagrams-
Edexcel AS/A2 Further Maths 2017Core Pure MathsArgand DiagramsArgand Diagrams-
I.B. Higher Level1Complex NumbersArgand diagram-
Methods (UK)M3Complex NumbersArgand diagram-
OCR A-Level (UK - Pre-2017)FP1Complex NumbersArgand diagram-
OCR AS Further Maths 2017Pure CoreArgand Diagrams and LociArgand Diagrams-
OCR MEI AS Further Maths 2017Core Pure AArgand Diagrams and LociArgand Diagrams-
OCR-MEI A-Level (UK - Pre-2017)FP1Complex NumbersArgand diagram-
Pre-U A-Level (UK)7Complex NumbersArgand diagram-
Scottish Advanced HighersM2Complex NumbersArgand diagram-
Scottish (Highers + Advanced)AM2Complex NumbersArgand diagram-
Universal (all site questions)CComplex NumbersArgand diagram-
WJEC A-Level (Wales)FP1Complex NumbersArgand diagram-