<PRE><B>Question 375707</B>
To solve this problem, we are going to use the FOIL method:
First - Multiply the first term in each set of parentheses
Outer - Multiply the outer term in each set of parentheses
Inner - Multiply the inner term in each set of parentheses
Last  - Multiply the last term in each set of parentheses

So for this problem:
(5 + 3i)*(6 - 2i)=
5(6) + (-5)(2i) + (3i)(6) + (3i)(-2i)=
30 - 10i + 18i - 6i^2
Now we know that since i = sqrt(-1), then i^2 = -1. So we can put this in the equation:
30 - 10i + 18i - 6(-1)=
30 - 10i + 18i + 6
Now we can combine like terms:
30 - 10i + 18i + 6=
36 + 8i
So your simplified answer is 36 + 8i.  
Hope this helps!</PRE>