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A-LevelMathematicsComplex numbers9709/32 · Feb/Mar 2023 · Q45 Marks

Solve the equation 5z / (1 + 2i) - zz* + 30 + 10i = 0, giving your answers in the form x + iy, where x and y are real.

  1. Solve the equation 5z / (1 + 2i) - zz* + 30 + 10i = 0, giving your answers in the form x + iy, where x and y are real.[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

  1. [B1] Substitute z = x + iy and z* = x - iy to obtain a correct equation, horizontal or with (1–2i)/( 1 – 2i) seen, in x and y
  2. [*M1] Use i² = –1 at least once and equate real and imaginary parts to zero OE For their horizontal equation.
  3. [A1] Obtain two correct equations e.g. x + 2y - x² - y² + 30 = 0 and −2x + y + 10 = 0
  4. [DM1] Solve quadratic equation for x or for y
  5. [A1] Obtain answers 3 – 4i and 6 + 2i

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About this question

Topic
Complex numbers, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2023 Paper 3 Variant 2, question 4.

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