Question

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

Answer 1

$|1-i{|}^x=2^x$
Here, $|1-i|=\sqrt{2}$
$\Rightarrow (2{)}^{\frac{x}{2}}=2^x$
$\Rightarrow \frac{2^x}{2^{\frac{x}{2}}}=1$
$\Rightarrow 2^{\frac{x}{2}}=2^0$
$\therefore x=0$
So, number of solutions is $1$.