A two-element array consisting of two isotropic antennas separated by a distance d along the z-axis is placed in a coordinate system whose z-axis points eastward and whose x-axis points toward the zenith. If a0 and a1 are the amplitudes of the excitations of the antennas at z = 0 and at z =d respectively, and if d is the phase of the excitation of the antenna at z =d relative to that of the other antenna, find the array factor and plot the pattern in the x–z plane for
(a) a0 = a1 = 1, = 4, and d = /2,
(b) a0 = a1 = 2, = 0, and d = 
(c) a0 = a1 = 1, = - 2, and d =
(d) a0 a1, a1 = 2, = and d =and
(e) a0 =a1, a1 = = and d =