A-LevelMathematicsComplex numbers9709/31 · Oct/Nov 2022 · Q54 Marks
The complex numbers u and w are defined by u = 2e^(πi/4) and w = 3e^(πi/3).
- (a)Find u²/w, giving your answer in the form re^(iθ), where r > 0 and −π < θ ≤ π. Give the exact values of r and θ.[3]
- (b)State the least positive integer n such that both Im wⁿ = 0 and Re wⁿ > 0.[1]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [B1] (a) State or imply u² = 4e^(πi/2)
- [B1] + [B1] (a) Obtain answer r = 4/3 and θ = π/6
- [B1] (b) State n = 6
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