The number of non-zero integral solution of the equation ${∣ ∣ \sqrt{3} + i ∣ ∣}^{x} = 2^{x}$

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Infinitely many

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None of these

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Solution

The correct option is C Infinitely many
Let $z = \sqrt{3} + i$

Hence $| z |$

$= | \sqrt{3} + i |$

$= \sqrt{(\sqrt{3})^{2} + 1}$

$= \sqrt{4}$

$= 2$

So, the left-hand side and right-hand side of the equation become equal.
Hence the above equation has infinitely many solutions.

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