User interface language: English | Español

Date May 2021 Marks available 1 Reference code 21M.2.AHL.TZ1.8
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number 8 Adapted from N/A

Question

Consider the complex numbers z=2cosπ5+isinπ5 and w=8cos2kπ5-isin2kπ5, where k+.

Suppose that zw.

Find the modulus of zw.

[1]
a.

Find the argument of zw in terms of k.

[2]
b.

Find the minimum value of k.

[3]
c.i.

For the value of k found in part (i), find the value of zw.

[1]
c.ii.

Markscheme

zw=16     A1

 

[1 mark]

a.

attempt to find argz+argw       (M1)

argzw=argz+argw

=π5-2kπ5=1-2kπ5       A1

 

[2 marks]

b.

zwargzw is a multiple of π       (M1)

1-2k is a multiple of 5       (M1)

k=3       A1

 

[3 marks]

c.i.

zw=16cos-π+isin-π

-16         A1

 

[1 mark]

c.ii.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Topic 1—Number and algebra » AHL 1.13—Polar and Euler form
Show 81 related questions
Topic 1—Number and algebra

View options