6 The complex number \(w\) is defined by \(w = - 1 + \mathrm { i }\).
- Find the modulus and argument of \(w ^ { 2 }\) and \(w ^ { 3 }\), showing your working.
- The points in an Argand diagram representing \(w\) and \(w ^ { 2 }\) are the ends of a diameter of a circle. Find the equation of the circle, giving your answer in the form \(| z - ( a + b \mathrm { i } ) | = k\).