Step 1: Find the modulus of the complex number (1 - i).

For a complex number a + bi, the modulus is |a + bi| = $\sqrt{a² + b²}$.

Therefore, |1 - i| = |1 + (-1)i| = $\sqrt{1² + (-1}$²) = $\sqrt{1 + 1}$ = $\sqrt{2}$.

Step 2: Substitute the value in the given equation.

The equation becomes: ($\sqrt{2}$)^x = $2^{x}$

Step 3: Express both sides with the same base.

Since $\sqrt{2}$ = 2^(1/2), we have: (2^(1/2))^x = $2^{x}$ 2^(x/2) = $2^{x}$

Step 4: Equate the exponents.

x/2 = x x - x/2 = 0 x/2 = 0 x = 0

Step 5: Apply the constraint.

The only solution is x = 0, but the question asks for non-zero integral solutions.

Therefore, the number of non-zero integral solutions = 0.