Connect the ideas.
- Use i squared equals negative one, and collect real and imaginary components separately.
- A complex number equals another only when both corresponding components agree.
- Multiply numerator and denominator by the denominator's conjugate to divide.
- A real quadratic's non-real roots come in conjugate pairs.
- Modulus is distance; it is a non-negative real number.
- Each complex root gives a linear factor over the complex numbers.
Put it together.
Choose a paper and show your working.
Complex numbers — practice test 1
Build from Cartesian components and arithmetic to quadratic roots, geometric distances and a short identity proof.
10 questions · 50 marks · 65 minutes · By handComplex numbers — practice test 2
Connect equations and factorisation with Argand geometry, midpoint conditions and real-parameter questions.
10 questions · 54 marks · 70 minutes · By handComplex numbers — applications test
Use fully specified position, calibration and electrical-style models; connect each model to exact Cartesian arithmetic and geometry.
10 questions · 57 marks · 70 minutes · By handComplex numbers — reasoning test
Use component equations, geometric constraints and short proofs to justify complex-number results.
10 questions · 56 marks · 75 minutes · By handComplex numbers — extended mixed test
Combine exact calculation, constraints, geometric reasoning and factorisation. Later questions require several linked ideas.
10 questions · 60 marks · 75 minutes · By hand
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 Mathematics, real and complex numbers: Cartesian arithmetic, conjugates, quadratic roots and Argand geometry. Polar form and roots of unity are developed in Year 12.
Official curriculum source ↗