MathDB

Let

x_0

x_1

x_2

, and

x_3

be complex numbers forming a square centered at

0

in the complex plane with side length

2

. For each

0\leq k\leq 3

, there are four more complex numbers

z_{4k}, z_{4k+1}

z_{4k+2}

, and

z_{4k+3}

forming a square centered at

x_k

with side length

\sqrt 2

. Given that

\prod_{i=0}^{15} z_i

is a positive integer, how many possible values could it take?
Proposed by Hari Desikan

Problem Statement