Question

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

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

Answer 1

The correct option is A

zero

Since1-i = $\sqrt{2}$ $[cos\frac{\pi }{4}-isin\frac{\pi }{4}]$, |1-i|

$\therefore$ $|1-i{|}^x$=$2^x$ $\Rightarrow$ ${\left(\sqrt{2}\right)}^x$=$2^x$ $\Rightarrow$ $2^{x/2}$ =$2^x$

$\Rightarrow$ $\frac{x}{2}$=x then x=0.

Therefore, the number of non-zero integral solutions is nil or Zero.