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

G Gautam harsolia

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  $\small |1-i|^x=2^x$

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