I have to show that the transformation, $\enspace z\to\frac{1}{z}\enspace$ , in the complex plane, transforms lines or circles in lines or circles (not respectively).
I'm completely new on complex plane, It's geometry and transformations. I've looked around and understood what the reciprocal of a complex number is and where it gets mapped to but I still don't see how you get a circle out of a line or vice versa.
EDIT: I have to use the following equations:
line: $$\enspace az\enspace+\enspace\overline{az}\enspace+\enspace c = 0\enspace\text { with } a\in\mathbb{C},\enspace b\in\mathbb{R}$$
circumference:$$az\overline{z}\enspace+\enspace bz\enspace+\enspace\overline{bz}\enspace+\enspace c = 0\enspace\text{ with }\enspace a, b\in\mathbb{C}, \enspace c\in\mathbb{R}$$