Year 11 / Unit 2
Read a complex number geometrically
The modulus is distance from the origin. An argument is an angle from the positive real axis; adding a full turn gives the same direction. Always inspect the quadrant before choosing an angle.
The expression |z − a| is the distance from z to a. A fixed distance produces a circle; equal distances from two points produce their perpendicular bisector.
Describe the locus |z − (2 + i)| = 3.
- The centre has Argand coordinates (2, 1).
- Every point is distance 3 from the centre, so the locus is a circle of radius 3.
Assumed knowledge
Write complex numbers in Cartesian form and locate them on an Argand diagram. Use Pythagoras’ theorem, trigonometry, angle quadrants, and basic circle and perpendicular-bisector geometry.
Study Specialist Mathematics alongside, or after, Mathematical Methods. Later units build on earlier units.
QCAA prior-learning guidance ↗