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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

z3w=5+5i.

Find w and z in the form a+bi where abZ.

Markscheme

substituting w=2iz into z3w=5+5i     M1

z6iz=5+5i      A1

let z=x+yi

comparing real and imaginary parts of (xyi)6i(x+yi)=5+5i     M1

to obtain x+6y=5 and 6xy=5      A1

attempting to solve for x and y)     M1

x=1 and y=1 so z=1+i      A1

hence w=22i      A1

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » AHL 1.12—Complex numbers – Cartesian form and Argand diag
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Topic 1—Number and algebra

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