Let
z=\dfrac{1+i}{\sqrt{2}}
What is
\left(z^{1^{2}}+z^{2^{2}}+z^{3^{2}}+\cdots+z^{12^{2}}\right) \cdot\left(\dfrac{1}{z^{1^{2}}}+\dfrac{1}{z^{2^{2}}}+\dfrac{1}{z^{3^{2}}}+\cdots+\dfrac{1}{z^{12^{2}}}\right) ?
Answer Choices
A. 18
B. 72-36 \sqrt{2}
C. 36
D. 72
E. 72+36 \sqrt{2}