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HSC-EXT2 · Complex Numbers

Complex Numbers

HSC HSC Mathematics Extension 2 · 2024 NESA Syllabus

MEX-N1MEX-N2
MEX-N1

Introduction to Complex Numbers

Define and perform arithmetic with complex numbers; represent on the Argand diagram; find modulus and argument.

Sample questions
  1. 1.Express (3 + 2i)/(1 − i) in the form a + bi.
  2. 2.Find the modulus and argument of z = −1 + i√3.
Exam weighting

3–5 marks.

Common student mistakes
  • ·Incorrect argument — failing to account for which quadrant the complex number lies in
  • ·Multiplying by the complex conjugate incorrectly
MEX-N2

Using Complex Numbers

Apply De Moivre's theorem; find nth roots of complex numbers; use complex numbers to prove trigonometric identities.

Sample questions
  1. 1.Use De Moivre's theorem to express cos(3θ) in terms of cosθ.
  2. 2.Find all fourth roots of 16i, expressing answers in polar form.
Exam weighting

4–6 marks — one of the most challenging topic areas.

Common student mistakes
  • ·Incorrect spacing of nth roots (arguments differing by 2π/n)
  • ·Not expressing roots in both Cartesian and polar form

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