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A-LevelMathematicsComplex numbers9709/32 · May/June 2021 · Q55 Marks

The complex number u is given by u = 10 – 4√6i. Find the two square roots of u, giving your answers in the form a + ib, where a and b are real and exact.

  1. The complex number u is given by u = 10 – 4√6i. Find the two square roots of u, giving your answers in the form a + ib, where a and b are real and exact.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [M1] Square a + ib, use i² = −1 and equate real and imaginary parts to 10 and −4√6 respectively
  2. [A1] Obtain a²−b² = 10 and 2ab = −4√6
  3. [M1] Eliminate one unknown and find an equation in the other
  4. [A1] Obtain a⁴−10a²−24[= 0], or b⁴+10b²−24[= 0], or 3-term equivalent
  5. [A1] Obtain final answers ±(2√3−√2i), or exact equivalents

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About this question

Topic
Complex numbers, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2021 Paper 3 Variant 2, question 5.

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