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

Solution:

It is given that |1 – i|ˣ = 2ˣ.

We know that |1 - i| = √[(1)² + (-1)²] = √2.

Using this the given equation becomes,

(√2)^x = 2^x

2^x/2 = 2^x

x/2 = x (Using the equality property of exponential equations)

There is only one real number x = 0 which satisfies this equation.

But the problem is asking for non-zero integral solutions which do not exist in this case.

Therefore, the number of non-zero integral solutions is 0

NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 18

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

Summary:

The number of non-zero integral solutions of the equation |1 – i|ˣ = 2ˣ is 0