2 Two loci, \(L _ { 1 }\) and \(L _ { 2 }\), in an Argand diagram are given by $$\begin{aligned} & L _ { 1 } : | z + 6 - 5 \mathrm { i } | = 4 \sqrt { 2 }
& L _ { 2 } : \quad \arg ( z + \mathrm { i } ) = \frac { 3 \pi } { 4 } \end{aligned}$$ The point \(P\) represents the complex number \(- 2 + \mathrm { i }\).

1. Verify that the point \(P\) is a point of intersection of \(L _ { 1 }\) and \(L _ { 2 }\).
2. Sketch \(L _ { 1 }\) and \(L _ { 2 }\) on one Argand diagram.
3. The point \(Q\) is also a point of intersection of \(L _ { 1 }\) and \(L _ { 2 }\). Find the complex number that is represented by \(Q\).