Find the number of non-zero integral solutions of the equation |1 – i| x = 2 x

Question

Philoid · Accepted Answer

We have equation as:

|1-i|^x = 2^x

(√2)^x = 2^x

2^x/2 = 2^x

On equating powers, we get:

x = 2x

2x - x = 0

x = 0

Hence, for the given solution 0 is the only integral solution.

Find the number of non-zero integral solutions of the equation |1 – i|x = 2x