Date | May Specimen paper | Marks available | 7 | Reference code | SPM.2.AHL.TZ0.8 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | 8 | Adapted from | N/A |
Question
The complex numbers w and z satisfy the equations
wz=2i
z∗−3w=5+5i.
Find w and z in the form a+bi where a, b∈Z.
Markscheme
substituting w=2iz into z∗−3w=5+5i M1
z∗−6iz=5+5i A1
let z=x+yi
comparing real and imaginary parts of (x−yi)−6i(x+yi)=5+5i M1
to obtain x+6y=5 and −6x−y=5 A1
attempting to solve for x and y) M1
x=−1 and y=1 so z=−1+i A1
hence w=−2−2i A1
[7 marks]
Examiners report
[N/A]