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
E) circle with centre at the origin
Correct Answer: A
Solution :
\[\arg [(1-2i)z-2+5i]=\frac{\pi }{4}\] \[\Rightarrow \]\[\arg [(1-2i)(x+iy)-2+5i]=\frac{\pi }{4}\] \[\Rightarrow \]\[\arg [(x+2y-2)+i(y-2x+5)]=\frac{\pi }{4}\] \[\Rightarrow \] \[{{\tan }^{-1}}\left[ \frac{y-2x+5}{x+2y-2} \right]=\frac{\pi }{4}\] \[\Rightarrow \] \[\frac{y-2x+5}{x+2y-2}=1\] \[\Rightarrow \] \[3x+y-7=0\] Which represents a line not passing through the origin.
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