Find the number of non-zero integral solutions of the equation |1 - i|

1.	Find the number of non-zero integral solutions of the equation \|1 - i\|x = 2x.
Answer» Given \|1 - i\|^x = 2^x ⇒ √(1 + 1)^x = 2^x 2^x/2 = 2^x ∴ x/2 = x ⇒ x = 0 ∴ There is no non-zero integral solution

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

Answer»

Given |1 - i|^x = 2^x

⇒ √(1 + 1)^x = 2^x

2^x/2 = 2^x

∴ x/2 = x ⇒ x = 0

∴ There is no non-zero integral solution