Find the number of non-zero integral solutions of the equation .

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Solution

The given expression is,

| 1−i | x = 2 x ( 1 2 + ( −1 ) 2 ) x = 2 x ( 2 ) x = 2 x 2 x 2 = 2 x

We know that if bases are same, then the powers are equal. Therefore,

x 2 =x 2x−x=0 x=0

The given equation has only 0 as the solution. Thus, the number of non-zero integral solutions is 0 .

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