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

Asked by Abhisek | 1 year ago |  154

#### 1 Answer

##### Solution :-

Equation

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

$$( \sqrt{1^2+(-1)^2})^x=2^x$$

$$(\sqrt{2})^x=2^x$$

$$2^{\dfrac{x}{2}}= 2^x$$

$$\dfrac{x}{2}=x$$

x = 2x

x = 0

Thus, 0 is the only integral solution of the given equation. Therefore, the number of nonzero integral solutions of the given equation is 0 .

Answered by Pragya Singh | 1 year ago

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