Question

Find non-zero integral solutions of $|1-i{|}^x=2^x$.

• A. $1$
• B. $2$
• C. $3$
• D. None of these

Answer 1

The correct option is D None of these

We have,

$|1-i{|}^x=2^x$

$(\sqrt{2}{)}^x=2^x$

$2^{x/2}=2^x$

$2^{x/2}=1$

$2^{x/2}=2^0$

$\frac{x}{2}=0$

$x=0$

Hence, the given equation has no non-zero integral solution.