Is this correct below?
$$ A \times B = (4 + i1) (2 + i3) $$
$$ = (4)(2) + (i1)(i3) + (i1)(2) + (4)(i3) $$
$$ = 8 + (i^2 3) + i(2) + (i12) $$
$$ = 8 +((-1)3) + i2 + i12 $$
$$= 8 + 3 + i2 + i12 $$
$$ = 11 + i14 $$
So $A \times B = 11 + 14i$.
Is this the correct answer and method of getting the right answer?
You made a simple mistake in the 5th line. It will be: $$8+((-1)3)+14i=8-3+14i=5+14i$$