Q. 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
Explanation
(b)
We have, $|1 - i|^{x} = 2^{x} \Rightarrow \left( \sqrt{2} \right)^{x} = 2^{x}$
$\Rightarrow \ 2^{x/2} = 2^{x}$
$\Rightarrow \ \frac{x}{2} = x\ \Rightarrow \ x = 0$
Therefore, the number of non-zero integral solution is one
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.