Complex numbers — Topic Review | Year 11

QUICK RECAP

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.

Complete each paper and show your working.

Complex numbers — practice test 1
10 questions · 50 marks · 65 minutes · By hand
Build from Cartesian components and arithmetic to quadratic roots, geometric distances and a short identity proof.
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Complex numbers — practice test 2
10 questions · 54 marks · 70 minutes · By hand
Connect equations and factorisation with Argand geometry, midpoint conditions and real-parameter questions.
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Complex numbers — applications test
10 questions · 57 marks · 70 minutes · By hand
Use fully specified position, calibration and electrical-style models; connect each model to exact Cartesian arithmetic and geometry.
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Complex numbers — reasoning test
10 questions · 56 marks · 75 minutes · By hand
Use component equations, geometric constraints and short proofs to justify complex-number results.
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Complex numbers — extended mixed test
10 questions · 60 marks · 75 minutes · By hand
Combine exact calculation, constraints, geometric reasoning and factorisation. Later questions require several linked ideas.
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