Question

The locus of $z$ such that $arg [(1 - 2i) z - 2 + 5i] = \frac {\pi} {4}$ is a

• A. line not passing through the origin
• B. circle not passing through the origin
• C. line passing through the origin
• D. circle passing through the origin

Answer 1

Answer: (A)

line not passing through the origin

Answer 2

$arg\left[\left(1-2i\right)\left(x+iy\right)-2+5i\right]=\frac{\pi}{4}$