I'm studying for this exam and one of the questions I am stuck on is:
Find the image of the line $$3x-y+1 = 0$$ under the transformation $$z \mapsto \frac{2}{z+1}$$
So I know I have to convert the formula for a line into complex form and then substitute the transformation into that formula. But I'm not quite sure how to do that.
Thanks!
The transformation is a Moebius transform, and as such it maps lines and circles to lines and circles. Any line or circle is characterized by knowing three points along it. So pick three points on your line, and see where they are mapped to by the transformation.