Numerical range of a matrix contains the convex hull of the eigenvalues.
The numerical range $W(A)$ is convex. This is a non-trivial fact, as far as I know, so maybe you are supposed to use this fact and not prove it.
The numerical range $W(A)$ is convex. This is a non-trivial fact, as far as I know, so maybe you are supposed to use this fact and not prove it.