- The complex number \(z\) is represented by the point \(P ( x , y )\) in an Argand diagram.
Two loci, \(L _ { 1 }\) and \(L _ { 2 }\), are given by:
$$\begin{aligned}
& L _ { 1 } : | z - 2 + \mathrm { i } | = | z + 2 - 3 \mathrm { i } |
& L _ { 2 } : | z - 2 + \mathrm { i } | = \sqrt { 10 }
\end{aligned}$$
- Find the coordinates of the points of intersection of these loci.
- On the same Argand diagram, sketch the loci \(L _ { 1 }\) and \(L _ { 2 }\). Clearly label the coordinates of the points of intersection.