Argand Diagrams (Cambridge (CIE) A Level Maths) : Revision Note

Argand Diagrams - Basics

What is an Argand diagram?

• An Argand diagram is a geometrical way to represent complex numbers as either a point or a vector in two-dimensional space

  • We can represent the complex number  by the point with cartesian coordinate 

• The real component is represented by points on the x-axis, called the real axis, Re

• The imaginary component is represented by points on the y-axis, called the imaginary axis, Im

• You may be asked to show roots of an equation in an Argand diagram

  • First solve the equation

  • Draw a quick sketch, only adding essential information to the axes

  • Plot the points and label clearly

How can I use an Argand diagram to visualise |z₁ + z₂| and |z₁ - z₂|?

• Plot two complex numbers z₁ and z₂

• Draw a line from the origin to each complex number

• Form a parallelogram using the two lines as two adjacent sides

• The modulus of their sum |z₁ + z₂| will be the length of the diagonal of the parallelogram starting at the origin

• The modulus of their difference |z₁ - z₂| will be the length of the diagonal between the two complex numbers