CIE A Level Maths: Pure 3复习笔记8.2.1 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 Argan 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