Q. The number of non-zero integer solutions of the equation $|1 - i|^{x} = 2^{x}$ is
A) Infinite
B) 1
C) 2
D) None of these
Explanation
(d)
Given, $|1 - i|^{x} = 2^{x}$
$\Rightarrow \ \ \ \left( \sqrt{1 + 1} \right)^{x} = 2^{x}\ \ \ \ \Rightarrow \ \ \ 2^{x/2} = 2^{x}$
$\Rightarrow \ \ \frac{x}{2} = x\ \ \ \ \ \Rightarrow \ \ \ \ x = 0$
Therefore, the number of non-zero integral solutions is zero
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.