The z-transform X(z) of a real and right-sided sequence x[n] has exactly two poles and one of them is at $$z = {e^{\frac{{i\pi }}{2}}}$$  and there are two zeros at the origin. If x(1) = 1, which one of the following is TRUE?

A. $$X\left( z \right) = \frac{{2{z^2}}}{{{{\left( {z - 1} \right)}^2} + 2}},\,{\text{ROC}}\,{\text{is}}\,\frac{1}{2} < \left| z \right| < 1$$

B. $$X\left( z \right) = \frac{{2{z^2}}}{{{z^2} + 1}},\,{\text{ROC}}\,{\text{is}}\,\left| z \right| > \frac{1}{2}$$

C. $$X\left( z \right) = \frac{{2{z^2}}}{{{{\left( {z - 1} \right)}^2} + 2}},\,{\text{ROC}}\,{\text{is}}\,\left| z \right| > 1$$

D. $$X\left( z \right) = \frac{{2{z^2}}}{{{z^2} + 1}},\,{\text{ROC}}\,{\text{is}}\,\left| z \right| > 1$$

Answer: Option D