⇒ Complex numbers can be used to represent a locus of points on an Argand diagram

⇒ Using the above result, you can replace z₂ with the general point z. The locus of points described by |z - z₁| = r is a circle with centre (x₁, y₁) and radius r

⇒ You can derive a Cartesian form of the equation of a circle from this form by squaring both sides:

⇒ The locus of points that are an equal distance from two different points z₁ and z₂ is the perpendicular bisector of the line segment joining the two points

⇒ Locus questions can also make use of the geometric property of the argument

⇒ You can find the Cartesian equation of the half-line corresponding to arg(z - z₁) = θ by considering how the argument is calculated:

⇒ Also see our notes on:

• Argand Diagrams
• Modulus and Argument
• Modulus-Argument Form of Complex Numbers
• Regions in the Argand Diagram