Question

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

• A. infinite
• B. 1
• C. 2
• D. None of these

Answer 1

Answer: (B)

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.