Complex Numbers

There are 3 complex numbers a+bi, c+di,e+fi. If b=3, e=-a-c, and the sum of the numbers is 2i, find d+f.

[a + bi ] + [ c + di] + [ e + fi]  =   2i

Therefore  

a + c + e  = 0  →   a + c + [-a -c]  = 0    which is true

And

b + d + f   = 2    and if b = 3, then

3 + (d + f)   = 2       subtract 3 from both sides

(d + f)   = - 1