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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.

Find w when

Point z on the Argand diagram can be transformed to point w by two transformations.

z=2i.

[2]
a.i.

z=1+i.

[1]
a.ii.

Describe these two transformations and give the order in which they are applied.

[3]
b.

Hence, or otherwise, find the value of z when w=2i.

[2]
c.

Markscheme

i2=-1              (M1)

w=-2+1=-1              A1


[2 marks]

a.i.

w=-1+i+1=i              A1


[1 mark]

a.ii.

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]

b.

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]

c.

Examiners report

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

Syllabus sections

Topic 1—Number and algebra » AHL 1.12—Complex numbers introduction
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