What is the sum of (5+3i) and (5-3i)

(5+3i)+(5-3i)= 10i
5+3i = 8i
5-3i  = 2i
8i+2i=10i

(Although I'm not sure why the "i" is needed if it is a real number)

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