IAL 2021 Oct Q3

A transformation maps points from the $z$-plane, where $z = x + \mathrm{i} y$ , to the $w$-plane, where $w = u + \mathrm{i} v$ . The transformation is given by

The transformation maps the imaginary axis in the $z$-plane onto the line $l$ in the $w$-plane.

Determine a Cartesian equation of $l$ , giving your answer in the form $au + bv + c = 0$ where $a$ , $b$ and $c$ are integers to be found.