Find the number of non-zero integral solutions of the equation:
\( |1 - i|^x = 2^2 \)
\( |1 - i| = \sqrt{1^2 + (-1)^2} = \sqrt{2} \)
\( (\sqrt{2})^x = 2^2 \)
\( 2^{x/2} = 2^2 \)
\( \frac{x}{2} = 2 \Rightarrow x = 4 \)
Since \( x = 4 \) is a non-zero integer, the number of non-zero integral solutions is 1.