2021HSCShort answer

Q11 (e)

2 marks

Question

The complex numbers $z=5+i$ and $w=2-4i$ are given. Find $\frac{\bar z}{w}$ , giving your answer in Cartesian form.

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Solution

Criteria	Marks
Provides correct solution	2
Identifies $\bar z$ , or equivalent merit	1

Sample answer:

$z=5+i,\qquad w=2-4i$
$\therefore\bar z=5-i$
$\frac{\bar z}{w}=\frac{5-i}{2-4i}\times\frac{2+4i}{2+4i}$
$=\frac{10+20i-2i+4}{4+16}=\frac{14+18i}{20}$
$=\frac7{10}+\frac9{10}i$

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Syllabus alignment

Complex Numbers

Arithmetic of complex numbersRepresent and calculate with complex numbers in Cartesian form, including conjugates, division, reciprocals and square roots.

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