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Question
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
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Solution
`|1-i|^x = 2^x`
⇒ `(sqrt(1^2 + (-1)^2))^x = 2^x`
⇒ `(sqrt2)^x = 2^x`
⇒ `2^(x/2) = 2^x`
⇒ `x/2 = x`
⇒ x = 2x
⇒ 2x - x = 0
⇒ x = 0
This equation cannot have any solution other than 0.
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