sum means to add together
you can think of the imaginary number "i" to be like a variable x
then its a matter of adding up like terms
the sum of (5+3i) and (5-3i) is
(5+3i)+(5-3i)
now, following pemdas and doing the parenthesis first, you'll notice that you cant add up a real and an imaginary number together, so you're done with the parenthesis, now you're left with
5+3i +5-3i
rearranging using commutative property
5+5+3i-3i
and now adding up like terms
5+5 = 10
3i-3i=0
so what you get is just
10
