Question

If the argument of $z-(2+3i)$ is $\frac{\pi }{4}$, then the locus of $z=x+iy$ is :

• A. $x+y+1=0$
• B. $2x+y+2=0$
• C. $x+y-1=0$
• D. $x-y+1=0$

Answer 1

The correct option is D $x-y+1=0$

Given,
$arg|z-(2+3i\left)\right|=\frac{\pi }{4}$
$\Rightarrow ta{n}^{-1}\left(\frac{y-3}{x-2}\right)=\frac{\pi }{4}$
$\Rightarrow \frac{y-3}{x-2}=1$
$\Rightarrow x-y+1=0$