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  4. The number of non-zero integral solutions of the equation |1 - i|x = 2x is

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Q. The number of non-zero integral solutions of the equation $|1 - i|^x = 2^x$ is

WBJEEWBJEE 2007

Solution:

Given, $|1-i|^{x}=2^{x}$
$\Rightarrow (\sqrt{1+1})^{x}=2^{x}$
$\Rightarrow 2^{x / 2}=2^{x}$
$\Rightarrow \frac{x}{2}=x$
$\Rightarrow x=0,2$
Therefore, the number of non-zero integral solutions is one.