Find the number of non-zero integral solutions of the equation |1 - i|^x = 2^x.

(√(1² + (-1)²))^x = 2^x

⇒ (√2)^x = 2^x

⇒ 2^x/2 = 2^x

⇒ x/2 = x

⇒ 2x - x = 0

⇒ x = 0

Thus, 0 is the only integral solution of the given equation. Therefore, the number of non-zero integral solutions of the given equation is 0.