[SOLVED] Graph of a line in the Argand plane

I am having a mental block about this. (Headbang)

Given the equation

$\displaystyle A z \bar{z} + \bar{E} z + D = 0$

and the condition A = 0 and D is a real constant and E is a complex constant, show that this equation represents a line in the complex plane. (The additional complexity is due to the second part of the problem: Given $\displaystyle A \neq 0$, A and D real constants, E a complex constant, and $\displaystyle E \bar{E} - AD > 0$ this is supposed to represent a circle.)

So using the condition I've got:

$\displaystyle \bar{E} z + D = 0$

Thus

$\displaystyle z = -\frac{D}{\bar{E}}$

This is supposed to be the equation of a line. But since D and E are constants, I would say that z is representing merely a point? What have I got wrong this time??

-Dan