Hello, this question is so much a "how to do it" as it is a "why did they do it that way?"

The problem is to find a condition on three complex numbers

showing that they are colinear in the Argand plain.

Obviously the condition is going to be that the slope through any two sets of points must be equal. In the work that I did I used the slope between points

and between

.

The book, however, went in a very screwy direction to my thinking. Their result is that the quantity

must be real for the points to be colinear. As it happens this condition is exactly the same as mine, just written in a much neater form.

But how the

would you go about doing this problem and say "Oh yeah! I'd get this..." Is there any significance to the fraction

that I'm not seeing? Why might the book have put the answer in this form?

Thanks!

-Dan