Answer
$5$
Work Step by Step
Note: the standard form of a complex number is $a+bi$ where $i = \sqrt -1$ and $a$ and $b$ are real numbers.
Note: $i^{2} = \sqrt -1\sqrt -1 = -1$
Note: $\sqrt x\sqrt y = \sqrt xy$.
$(\sqrt 3 + i\sqrt 2)(\sqrt 3 - i\sqrt 2)$
Expand out the complex number:
$(\sqrt 3)^{2}-i\sqrt 3\sqrt 2+i\sqrt 2\sqrt 3 -i^{2}(\sqrt 2)^{2}$
As seen in the note above, $i^{2} = -1$, so substitute in $-1$.
$(\sqrt 3)^{2}-i\sqrt 3\sqrt 2+i\sqrt 2\sqrt 3 -(-1)(\sqrt 2)^{2}$
Simplify:
$(\sqrt 3)^{2}-i\sqrt 3\sqrt 2+i\sqrt 2\sqrt 3 +(\sqrt 2)^{2}$
$3-i\sqrt 3\sqrt 2+i\sqrt 2\sqrt 3 +2$
As seen in the note above, $\sqrt x\sqrt y = \sqrt xy$, so simplify further:
$3-i\sqrt 6+i\sqrt 6 +2$
Combine like terms, to express the complex number in standard form:
$5$
