(4 pts) The far field E of a circular loop with non-uniform current and C = lambda is approximated as E_{\infty}=A_{0} \cos ^{2}(\theta) e^{-j k} / r 0^{\circ}<\theta<90^{\circ} \text {

and } 0^{\circ}<\omega<360^{\circ} a) Find the maximum directivity of the loop. b) Estimate the input impedance of the loop.