A-LevelMathematicsComplex numbers9709/32 · Oct/Nov 2024 · Q54 Marks
The complex number u is given by u = (cos(⅓π) + i sin(⅓π))⁴ / (cos(½π) - i sin(½π)). Find the exact value of arg u.
- (a)The complex number u is given by u = (cos(⅓π) + i sin(⅓π))⁴ / (cos(½π) - i sin(½π)). Find the exact value of arg u.[2]
- (b)The complex numbers u and u* are plotted on an Argand diagram. Describe the single geometrical transformation that maps u onto u* and state the exact value of arg u*.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [M1] SOI
- [A1] Obtain arg u = 5π/7
- [B1] Reflection (in the) real axis
- [B1FT] FT their exact (a). Accept 2π- their exact (a). Accept an 'exact' expression in place of an exact value.
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