7. $$f ( z ) = z ^ { 4 } + a z ^ { 3 } + b z ^ { 2 } + c z + d$$ where \(a\), \(b\), \(c\) and \(d\) are real constants.
The equation \(\mathrm { f } ( \mathrm { z } ) = 0\) has complex roots \(\mathrm { z } _ { 1 } , \mathrm { z } _ { 2 } , \mathrm { z } _ { 3 }\) and \(\mathrm { z } _ { 4 }\) When plotted on an Argand diagram, the points representing \(z _ { 1 } , z _ { 2 } , z _ { 3 }\) and \(z _ { 4 }\) form the vertices of a square, with one vertex in each quadrant.
Given that \(z _ { 1 } = 2 + 3 i\), determine the values of \(a , b , c\) and \(d\).