Question

If Im $\left(\frac{z-i}{2i}\right)=0$ , then the locus of $z$ is:

• A. x-axis
• B. y- axis
• C. the line $x=y$
• D. The line $x+y+1=0$

Answer 1

Answer: (B)

y- axis

Let $z=x+iy$

$Im\left(\frac{x+iy-i}{2i}\right)=$$Im$$\left(\frac{1}{2}\right(-xi+y+1\left)\right)$

$=\frac{-x}{2}$
$\Rightarrow x=0$
which is the y - axis.