Numerical range of a linear transformation

Suppose T is a linear transformation on a finite-dimensional complex inner-product space V. Let I denote the identity transformation on V. The numerical range of T is the subset of C defined by

W(T)={T(x),x|xV,x=1}.
  1. Show that W(T+cI)=W(T)+c for every cC.
  2. Show that W(cT)=cW(T) for every cC.
  3. Show that the eigenvalues of T are contained in W(T).
  4. Let B be an orthonormal basis for V. Show that the diagonal entries of [T]B are contained in W(T).