- The complex number \(z = x + i y\) satisfies the equation
$$| z - 3 - 4 i | = | z + 1 + i |$$
- Determine an equation for the locus of \(z\) giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers.
- Shade, on an Argand diagram, the region defined by
$$| z - 3 - 4 i | \leqslant | z + 1 + i |$$
You do not need to determine the coordinates of any intercepts on the coordinate axes.