A-LevelFurther MathematicsComplex NumbersOct/Nov 2013Paper 1 Q1114 Marks
Answer only one of the following two alternatives. EITHER State the fifth roots of unity in the form cos θ + i sin θ, where –π < θ ≤ π. Simplify (x − [cos(π/5) + i sin(π/5)]) (x − [cos(π/5) − i sin(π/5)]). Hence find the real factors of x⁵ - 1. Express the six roots of the equation x⁶ - x³ + 1 = 0 as three conjugate pairs, in the form cos θ ± i sin θ. Hence find the real factors of x⁶ - x³ + 1.
✓ Correct Answer
The correct answer is —. This question tests the candidate's understanding of complex numbers within the Further Mathematicssyllabus. The examiner's mark scheme requires...
📋 Examiner Report & Trap Analysis
Common mistake: 62% of candidates selected the distractor because they confused... The examiner specifically designed this question to test whether students can differentiate between... To secure full marks, candidates must demonstrate...
🔒
Unlock the Examiner's Answer
Sign up for free to reveal the correct answer, the official mark scheme breakdown, and the examiner trap analysis for this question.
Sign Up Free to Unlock →Join thousands of Cambridge students already using Oracle Prep