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

Q : 18     Find the number of non-zero integral solutions of the equation  \small |1-i|^x=2^x .

Answers (1)

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Given problem is 
\small |1-i|^x=2^x
Now,
( \sqrt{1^2+(-1)^2 })^x=2^x
( \sqrt{1+1 })^x=2^x
\left ( \sqrt{2 }\right )^x=2^x
2^{\frac{x}{2}}= 2^x
\frac{x}{2}=x
\frac{x}{2}=0
x = 0  is the only possible solution to the given problem

Therefore, there are  0 number of  non-zero integral solutions of the equation  \small |1-i|^x=2^x 

Posted by

Gautam harsolia

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