Yes/No Is $p^2 \le y^2$?

Question

Given $z= x+iy$ and $m= p + iq$ be complex number such that $p^2 = z^2 +1 $

Is the following inequalities always True ? Yes/No

$p^2 \le y^2$

My attempt : I think No , take $y=0$ , $p=1$

Is its correct ?

Answer 1

You cannot just say “take $y=0$, $p=1$” without defining $z$. But, if you take $x=0$ too, then $z=x+yi=0$ and, indeed, $p^2=z^2+1$. And then, yes, $p^2>y^2$.