Date | May 2021 | Marks available | 2 | Reference code | 21M.1.AHL.TZ1.9 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Hence or otherwise | Question number | 9 | Adapted from | N/A |
Question
Consider w=iz+1, where w, z∈ℂ.
Find w when
Point z on the Argand diagram can be transformed to point w by two transformations.
z=2i.
z=1+i.
Describe these two transformations and give the order in which they are applied.
Hence, or otherwise, find the value of z when w=2−i.
Markscheme
i2=-1 (M1)
w=-2+1=-1 A1
[2 marks]
w=-1+i+1=i A1
[1 mark]
EITHER
rotation of 90° (anticlockwise, centre at the origin) A1A1
Note: Award A1 for “rotation” and A1 for “90°”.
followed by a translation of (10) A1
OR
translation of (0-1) A1
followed by rotation of 90° (anticlockwise, centre at the origin) A1A1
Note: Award A1 for “rotation” and A1 for “90°”.
[3 marks]
EITHER
move 1 to left to 1-i (M1)
then rotate by -90° to
-1-i A1
OR
iz+1=2-i
iz=1-i
z=1-ii (M1)
-1-i A1
[2 marks]