Question 93
Let complex sequence $\{z_n\}$ satisfy
$$
z_1 = \frac{\sqrt{3}}{2}, \quad z_{n+1} = \overline{z_n}(1 + z_n i) \quad (n = 1, 2, \dots),
$$
where $i$ is the imaginary unit. Find the value of $z_{2021}$.
$$
z_1 = \frac{\sqrt{3}}{2}, \quad z_{n+1} = \overline{z_n}(1 + z_n i) \quad (n = 1, 2, \dots),
$$
where $i$ is the imaginary unit. Find the value of $z_{2021}$.