The number of non-zero integral solutions of | vedclass

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(D) Given the equation $|1 - i|^x = 2^x$. First,calculate the modulus of the complex number $1 - i$: $|1 - i| = \sqrt{1^2 + (-1)^2} = \sqrt{2}$. Subst

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(D) Given the equation $|1 - i|^x = 2^x$. First,calculate the modulus of the complex number $1 - i$: $|1 - i| = \sqrt{1^2 + (-1)^2} = \sqrt{2}$. Substitute this into the equation: $(\sqrt{2})^x = 2^x$. This can be written as: $(2^{1/2})^x = 2^x$ $2^{x/2} = 2^x$. Equating the exponents: $\frac{x}{2} = x$ $x = 0$. The only solution is $x = 0$,which is not a non-zero integer. Therefore,the number of non-zero integral solutions is $0$.

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

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