Question:medium

\(\text{Find the number of non-zero integral solutions of the equation }|1-i|^x=2^2.\)

Updated On: Jan 22, 2026
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Solution and Explanation

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.
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