Part a) Let z and w be complex numbers satisfying |z| = 4 and |w| = 2. What is \(|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \)?
Part b) Let z and w be complex numbers satisfying |z| = 5, |w| = 2, and \(z\overline{w} = 6+8i.\) What is \(|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \)?