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

The correct option is D None of these

Since, $1-i=\sqrt{2}\{\cos \frac{\pi }{4}-i\sin \frac{\pi }{4}\}$
$\Rightarrow |1-i|=\sqrt{2}$
Given : ${|1-i|}^x=2^x$
$\Rightarrow {\left(\sqrt{2}\right)}^x=2^x$
$\Rightarrow \frac{x}{2}=x$
$\Rightarrow$ $2=1$

Hence, option D is correct.