Question

If $arg(z-2-3i)=\frac{\pi }{2}$ , then the equation to the locus of z is:

• A. $x=0$
• B. $x=1$
• C. $x=2$
• D. $x=3$

Answer 1

The correct option is C $x=2$

Let $z=x+iy$

$arg(z-2-3i)=\frac{\pi }{2}$

${\tan }^{-1}\left(\frac{y-3}{x-2}\right)=\frac{\pi }{2}$

$\Rightarrow x-2=0$

$\Rightarrow x=2$