A-LevelMathematicsComplex numbers9709/33 · May/June 2024 · Q35 Marks
The square roots of 24-7i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a quartic equation in x or y, find the square roots of 24-7i in exact Cartesian form.
- The square roots of 24-7i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a quartic equation in x or y, find the square roots of 24-7i in exact Cartesian form.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [M1] Square x + iy obtaining three terms when simplified and equate real and imaginary parts to 24 and -7 respectively
- [A1] Obtain equations x² – y² = 24 and 2xy = −7
- [M1] Eliminate one variable by correct method and find a horizontal equation in the other
- [A1] Obtain 4x⁴ – 96x² – 49 = 0 or 4y⁴ + 96y² – 49 = 0 or 3-term equivalents
- [A1] Obtain answers (7√2/2 + i√2/2) and (-7√2/2 - i√2/2) or exact equivalents and no others
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