The z-transform for discrete-time signals is the counterpart of the Laplace transform for continuoustime signals, and they each have a similar relationship to the corresponding Fourier transform. One motivation for introducing this generalization is that the Fourier transform does not converge for all sequences, and it is useful to have a generalization of the Fourier transform that encompasses a broader class of signals. A second advantage is that in analytical problems, the z-transform notation is often more convenient than the Fourier transform notation. Given that the z-transform of a sequence x[n] is X(z)=n=x[n]zn, (a) Find the z-transform X(z) of sequence x[n]=anu[n] ( a denotes a real or complex number) and graph the pole-zero plot of the sequence. (b) Find the z-transform X(z) of sequence x[n]=anu[n1] ( a denotes a real or complex number) and graph the pole-zero plot of the sequence. (c) Find the z-transform X(z) of sequence x[n]=(21)nu[n]+(31)nu[n] and graph the pole-zero plot of the sequence. (d) Find the z-transform X(z) of sequence x[n]=(31)nu[n](21)nu[n1] and graph the pole-zero plot of the sequence