9.
$$z = \frac { 1 } { 5 } - \frac { 2 } { 5 } \mathrm { i }$$
- Find the modulus and the argument of \(z\), giving the modulus as an exact answer and giving the argument in radians to 2 decimal places.
Given that
$$\mathrm { zw } = \lambda \mathrm { i }$$
where \(\lambda\) is a real constant,
- find \(w\) in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real. Give your answer in terms of \(\lambda\).
- Given that \(\lambda = \frac { 1 } { 10 }\)
- find \(\frac { 4 } { 3 } ( z + w )\),
- plot the points \(A , B , C\) and \(D\), representing \(z , z w , w\) and \(\frac { 4 } { 3 } ( z + w )\) respectively, on a single Argand diagram.