A-LevelMathematicsComplex numbers9709/32 · Feb/Mar 2022 · Q66 Marks
Find the complex numbers w which satisfy the equation w² + 2iw* = 1 and are such that Re w ≤ 0. Give your answers in the form x + iy, where x and y are real.
- (a)Find the complex numbers w which satisfy the equation w² + 2iw* = 1 and are such that Re w ≤ 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 (Feb/Mar 2022). The mark or mark type is shown in brackets.
- [1] Substitute and obtain a correct equation in x and y ((x + iy)² + 2i(x – iy) = 1)
- [1] Use i² = – 1 at least once and equate real and imaginary parts
- [1] Obtain two correct equations, e.g. x² – y² + 2y = 1 and 2xy + 2x = 0
- [1] Solve for x or for y
- [1] Using y = – 1, obtain answer w = – 2 – i only
- [1] Using x = 0, obtain answer w = i
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