7. The quadratic equation
$$z ^ { 2 } + 10 z + 169 = 0$$
has complex roots \(z _ { 1 }\) and \(z _ { 2 }\).
- Find each of these roots in the form \(a + b \mathrm { i }\).
- Find the modulus and argument of \(z _ { 1 }\) and of \(z _ { 2 }\).
Give the arguments in radians to 3 significant figures.
- Illustrate the two roots on a single Argand diagram.
- Find the value of \(\left| z _ { 1 } - z _ { 2 } \right|\).