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Complex numbers 2 — Question 7

QCAA 2025, Paper 2 · 1 mark

Q7 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 7

Given the complex number

z=\operatorname{cis}\!\left(-\frac{\pi}{2}\right)

, determine

\operatorname{Arg}(z^6)

.

(A)

\pi

(B)

0

(C)

-\pi

(D)

-3\pi

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

A —

\pi

Worked solution

By De Moivre’s theorem,

z^6=\operatorname{cis}(-3\pi)=-1

. The principal argument of

-1

is

\pi

(using

-\pi<\operatorname{Arg}(z)\leq\pi

).

Selects option A.

[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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