Date | May 2021 | Marks available | 3 | Reference code | 21M.1.AHL.TZ2.12 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Find | Question number | 12 | Adapted from | N/A |
Question
It is given that z1=3 cis(3π4) and z2=2 cis(nπ16), n∈ℤ+.
In parts (a)(i) and (a)(ii), give your answers in the form reiθ, r≥0, −π<θ≤π.
Find the value of z13.
Find the value of (z1z2)4 for n=2.
Find the least value of n such that z1z2∈ℝ+.
Markscheme
z13=27eiπ4 (=27e0.785398… A1A1
Note: Award A1 for and A1 for the angle in the correct form.
[2 marks]
A1A2
Note: Award A1 for , A2 for the angle in the correct form and A1 for the angle in incorrect form e.g. and/or . Award A1 if is given in place of .
[3 marks]
(M1)
(M1)
A1
[3 marks]