The complex number \(w\) has modulus \(r\) and argument \(\theta\), where \(0<\theta<\frac12\pi\), and \(w^*\) denotes the conjugate of \(w\). State the modulus and argument of \(p\), where \(p=\frac w{w^*}\).[2]
Given that \(p^5\) is real and positive, find the possible values of \(\theta\).[2]
The complex number \(z\) satisfies the relations \(|z|\leq6\) and \(|z|=|z-8-6\mathrm i|\).
Illustrate both of these relations on a single Argand diagram.[3]
Find the greatest and least possible values of \(\arg z\), giving your answers in radians correct to 3 decimal places.[4]