Question 21
Let $$
z = \dfrac{1 + i}{\sqrt{2}}.
$$ What is
$$
\begin{aligned} &\left(z^{1^2} + z^{2^2} + z^{3^2} + \cdots + z^{12^2}\right) \\ &\quad {}\cdot \scriptsize \left(\dfrac{1}{z^{1^2}} + \dfrac{1}{z^{2^2}} + \dfrac{1}{z^{3^2}} + \cdots + \dfrac{1}{z^{12^2}}\right)? \end{aligned}
$$
z = \dfrac{1 + i}{\sqrt{2}}.
$$ What is
$$
\begin{aligned} &\left(z^{1^2} + z^{2^2} + z^{3^2} + \cdots + z^{12^2}\right) \\ &\quad {}\cdot \scriptsize \left(\dfrac{1}{z^{1^2}} + \dfrac{1}{z^{2^2}} + \dfrac{1}{z^{3^2}} + \cdots + \dfrac{1}{z^{12^2}}\right)? \end{aligned}
$$