Question

ATTENTION

Answer 1

Here!

The answer is Option A!

$(x + 2 \sqrt{3} i)(x - 2 \sqrt{3}i )$

Why so??

Let's see what complex numbers are!

$(x + 2 \sqrt{3 }i )(x - 2 \sqrt{3}i ) \\ = {x}^{2} - 2 \sqrt{3} x + 2 \sqrt{3} x - {(2 \sqrt{3} i)}^{2} \\ = {x}^{2} - {(2 \sqrt{3}i) }^{2}$

Now we know,

${i}^{2} = - 1$

So!

$= {x}^{2} - 12 \times( - 1)$

$= {x}^{2} + 12$

And thus we get the answer!