2020HSCShort answer

Q13 (d) (i)

1 mark

Question

Show that for any integer $n$ ,
$e^{in\theta}+e^{-in\theta}=2\cos(n\theta).$

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Solution

Criteria	Marks
Provides correct solution	1

Sample answer:

e^{in\theta}+e^{-in\theta}=(\cos n\theta+i\sin n\theta)+(\cos n\theta-i\sin n\theta)=2\cos(n\theta)

Supplied marking guidance · human reviewed

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Syllabus alignment

Working MathematicallyComplex Numbers

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

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