Complex numbers 2 — Question 10

QCAA 2020, Paper 1 · 1 mark

Q10 · 2020 · Technology-freeSimple familiar1 mark

QUESTION 10

The subset of the complex plane that represents

\arg(z+i-1)+\frac{\pi}{4}=0

for

z\in\mathbb C

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

z+i-1=z-(1-i)

, so the ray starts at

1-i

. The equation gives

\arg(z-(1-i))=-\pi/4

, so the ray points down and to the right from the open point

1-i

, which is option B.

Selects option B.

[1 mark]

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