Perform basic operations on complex numbers in a language without native support for complex numbers
APL (33 + 16 + 1 + 1 + 14 + 17 = 82)

APL does have support for complex numbers if you use it (of the format 5J6, like Python's 5+6j), but it is of course not used. 

I represent complex numbers as a 2-tuple of regular numbers, (A B) where A is the real part and B is the imaginary part. This means I can use APL's + and - operators directly, as they can be used on multidimensional types. (i.e. 1+2 3 4 gives 3 4 5 and 1 2+20 10 gives 21 12).

An APL function is represented as {body}. Functions are first-class objects. I have counted the function body without the braces, except for + and - which I've counted as 1 each.

read  ← {⎕ML←3⋄(1,1-2×'-'∊⍵)×⍎¨⍵⊂⍨⍵∊'.',⎕D} ⍝ 33 chars
print ← {⍕(⊃⍵)'+'(⊃⌽⍵)'i'}                   ⍝ 16 chars
add   ← +                                      ⍝ 1 char
sub   ← -                                      ⍝ 1 char
mul   ← {(-/⍺×⍵),+/⍺×⌽⍵}                      ⍝ 14 chars
div   ← {⍺mul 1 ¯1×⍵÷+/⍵*2}                   ⍝ 17 chars


Usage:
(clarification: APL is evaluated right-to-left so this is actually calculating 8+9i ÷ 5+6i.)

      print (read⍞) div (read⍞)
5 + 6i
8 + 9i
1.540983607 + ¯0.04918032787 i