MathNet 2021 — Part 02 Question 79

Complex numbers $z_1, z_2, \dots, z_{100}$ satisfy $z_1 = 3 + 2i$, $z_{n+1} = \overline{z_n} \cdot i^n$, ($n = 1, 2, \dots, 99$), with $i$ as the imaginary unit. Then the value of $z_{99} + z_{100}$ is ______.