Question

If $z=x+iy$ satisfies amp $(z-1)=\text{amp}(z+3i)$ then the value of $(x-1):y$ is equal to

• A. $2:1$
• B. $-1:3$
• C. $1:3$
• D. None of these

Answer 1

Answer: (C)

We have, $\text{amp}(z-1)=\text{amp}(z+3i)$
$\Rightarrow {\tan }^{-1}\frac{y}{x-1}={\tan }^{-1}\frac{y+3}{x}$
$\Rightarrow xy=(x-1)(y+3)$
$\Rightarrow 3(x-1)=y$
$\therefore (x-1):y=1:3.$