2021HSCShort answer

Q11 (a)

2 marks

Question

The complex numbers $z=2e^{i\pi/2}$ and $w=6e^{i\pi/6}$ are given. Find $zw$ , giving the answer in the form $re^{i\theta}$ .

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Solution

Criteria	Marks
Provides correct solution	2
Finds the correct argument	1

Sample answer:

$zw=(2\times6)e^{i\left(\frac\pi2+\frac\pi6\right)}=12e^{\frac{2\pi i}{3}}$

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Syllabus alignment

Complex Numbers

Other representations of complex numbersUse Euler's formula and convert between Cartesian, polar and exponential forms to solve problems.

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