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