1, Let z and w be complex numbers satisfying \(|z| = 4\) and |w| = 2 Then enter in the numbers \(|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \) below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark.

2, Let z and w be complex numbers satisfying |z| = 5, |w| = 2, and \(z\overline{w} = 6+8i.\) Then enter in the numbers \(|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \) below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark.

3,Consider the complex numbers in the following picture, as well as the line segments connecting them to the origin:

(a)Put the complex numbers u,v,w,z

in order of increasing magnitude, and enter them in below in that order.

(b)Put the complex numbers v-u,w-v,z-w,u-z

in order of increasing magnitude, and enter them in below in that order.

\(\)

Potatoes May 20, 2020