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2022 Mathematics Extension 2 Q2 | HSC Atlas

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2022TrialMultiple choice

Q2

1 mark

Question

Given that $z^n=a+bi$ and $|z|=1$ , where $a$ and $b$ are real, which of the following is equal to $z^{-n}$ ?

A. $a+bi$

B. $a-bi$

C. $-a+bi$

D. $-a-bi$

Try the question before revealing the answer.

Solution

B. Since $|z|=1$ , $z^{-n}=\frac{1}{z^n}=\frac{1}{a+bi}=a-bi$ (as $a^2+b^2=1$ ).

AI HSC Engine generated solution · human reviewed

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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.

Source

Fort St 2022 4U Trial PaperFort StQuestion paper page 2View original source ↗

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