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.Express (3 + 2i)/(1 − i) in the form a + bi.
- 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.Use De Moivre's theorem to express cos(3θ) in terms of cosθ.
- 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
Other Extension 2 topics
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