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A-LevelMathematicsComplex numbers9709/32 · Feb/Mar 2024 · Q36 Marks

It is given that z = -√3 + i.

  1. (a)Express z² in the form re^(iθ), where r > 0 and -π < θ ≤ π.[3]
  2. (b)The complex number ω is such that z²ω is real and |z²/ω³| = 12. Find the two possible values of ω, giving your answers in the form Re^(iα), where R > 0 and -π < α ≤ π.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

  1. [B1] Obtain r = 4
  2. [M1] Correct method for the argument
  3. [A1] Obtain θ = -π/3
  4. [M1] Use of α + their θ = 0 or α + their θ = -π or α + their θ = π
  5. [M1] Use of R = their r / 12
  6. [A1] Obtain (1/3)¹/³e^(iπ/3) and (1/3)¹/³e^(-i2π/3)

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About this question

Topic
Complex numbers, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Feb/Mar 2024 Paper 3 Variant 2, question 3.

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