Date | November 2018 | Marks available | 5 | Reference code | 18N.1.AHL.TZ0.H_11 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 0 |
Command term | Express and Find | Question number | H_11 | Adapted from | N/A |
Question
Let S be the sum of the roots found in part (a).
Find the roots of which satisfy the condition , expressing your answers in the form , where , .
Show that Re S = Im S.
By writing as , find the value of cos in the form , where , and are integers to be determined.
Hence, or otherwise, show that S = .
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
use of De Moivre’s theorem (M1)
(A1)
, (A1)
1, 2, 3, 4, 5
or or or or A2
Note: Award A1 if additional roots are given or if three correct roots are given with no incorrect (or additional) roots.
[5 marks]
Re S =
Im S = A1
Note: Award A1 for both parts correct.
but , , , and M1A1
⇒ Re S = Im S AG
Note: Accept a geometrical method.
[4 marks]
M1A1
A1
[3 marks]
(M1)
Note: Allow alternative methods eg .
(A1)
Re S =
Re S = A1
A1
S = Re(S)(1 + i) since Re S = Im S, R1
S = AG
[4 marks]