Divide and simplify(104i)/(3+i) express a in a + bi form

Here we're dividing, but what actually happens is that we get the " i " out of the denominator:

104i        104i       3-i        312i + 104      312i + 104
= * = =
 3+i        3+i          3-i            9+1                  10

Note that 3-i is the "conjugate" of 3+i.