Answer
$7+0i$
Work Step by Step
We are given the expression $(\sqrt 3+2i)(\sqrt 3-2i)$. We can use the FOIL method to simplify.
F=$\sqrt 3\times\sqrt 3=(\sqrt 3)^{2}=3$
O=$\sqrt 3\times-2i=-2i\sqrt 3$
I=$2i\times\sqrt 3=2i\sqrt 3$
L=$2i\times-2i=-4i^{2}=-4\times-1=4$
Now,we can combine these terms.
$(3)+(-2i\sqrt 3)+(2i\sqrt 3)+(4)=7=7+0i$
We know that $i^{2}=-1$.
