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

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

(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)