A-LevelMathematicsComplex numbers9709/33 · Oct/Nov 2025 · Q76 Marks
Solve the equation (5z)/(2-i) - zz* + 20+8i = 0. Give your answers in the form x+iy, where x and y are real.
- (a)Solve the equation (5z)/(2-i) - zz* + 20+8i = 0. Give your answers in the form x+iy, where x and y are real.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- Attempt to remove fraction by multiplying throughout by 2-i or multiply fraction by (2+i)/(2+i)
- Substitute z = x + iy and z* = x – iy throughout the equation
- Use i² = –1 correctly at least once and equate real and imaginary parts to zero
- Obtain two correct equations e.g. 5x – 2(x² + y²) + 48 = 0 and 5y + (x² + y²) – 4 = 0
- Solve a quadratic and a linear equation for x or for y
- Obtain answers 2 – 5i and 16/5 - 12/5 i only
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