Complex numbers 2 — Question 7

QCAA 2025, Paper 1 · 1 mark

Q7 · 2025 · Technology-freeSimple familiar1 mark

QUESTION 7

For

z\in\mathbb C

, a subset of the complex plane of the form

\operatorname{Arg}(z-z_1)=\theta

is shown.

The values of

z_1

and

\theta

respectively are

(A)

-i

and

-\dfrac{\pi}{4}

(B)

-i

and

\dfrac{\pi}{4}

(C)

i

and

-\dfrac{\pi}{4}

(D)

i

and

\dfrac{\pi}{4}

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

The ray starts at

z_1=i

. From that point it points down and right at angle

-\pi/4

from the positive real axis, so

z_1=i

and

\theta=-\pi/4

Selects option C.

[1 mark]

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