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Complex numbers 2 — Question 8

QCAA 2021, Paper 2 · 1 mark

Q8 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 8

The imaginary part of

\left(\operatorname{cis}\left(\frac{\pi}{8}\right)\right)^{-2}

is

(A)

-6.83

(B)

-0.71

(C)

0.71

(D)

1.17

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

B

Worked solution

By De Moivre’s theorem,

\operatorname{cis}(\pi/8)^{-2}=\operatorname{cis}(-\pi/4)

. Its imaginary part is

\sin(-\pi/4)=-\sqrt2/2\approx-0.71

.

Selects option B.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

View the full QCAA marking guide

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