Question

If $ampz=\frac{\pi }{4}$ then locus of z is

• A. y = 0
• B. x = 0
• C. y = x
• D. x + y = 0

Answer 1

The correct option is C y = x

Let $z=x+iy$
amp(z)$={\tan }^{-1}\left(y/x\right)=\pi /4$
$y/x=1$
$\therefore y=x$
$\therefore$ z lies on the line $y=x$