+23252 There are several ways to approach this; I'm going to rationalize the denominator of each term first.
[ 1 / (1 + 2i) ] · [ (1 - 2i) / (1 - 2i) ] = (1 - 2i) / 5
[ 3 / (1 - i) ] · [ (1 + i) / (1 + i) ] = 3(1 + i) / 2
[ (3 -2i) / (1 + 3i) ] · [ (1 - 3i) / (1 - 3i) ] = (-3 - 11i) / 10
[ 1 / (1 + 2i) + 3 / (1 - i) ] = [ (1 - 2i) / 5 + 3(1 + i) / 2 ] = (17 + 11i) / 10
[ (17 + 11i) / 10 ] · [ (-3 - 11i) / 10 ] = (70 - 220i) / 100 = 7/10 - (11/5)i
