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# 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

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