The number of integer solutions of the equation 1 - i x = 2 x is

The number of integer solutions of the equation

{|1 - i|}^{x} = 2^{x}

is

$1$
$0$
$2$
$3$

Solution

Given ${|1 - i|}^{x} = 2^{x}$
i.e. $2^{\frac{x}{2}} = 2^{x}$
$2^{\frac{x}{2}} = 1 = 2^{0} \Rightarrow x = 0$
Hence, only one integral solution.

Asked in: AP EAMCET 2022 (04 Jul Shift 1)

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