# Thread: [SOLVED] Graph of a line in the Argand plane

1. ## [SOLVED] Graph of a line in the Argand plane

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

2. Originally Posted by topsquark

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
Hi there topsquark.

Little wonder you're head banging. The question is flawed. The equation should be:

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

3. Originally Posted by mr fantastic
Hi there topsquark.

Little wonder you're head banging. The question is flawed. The equation should be:

$\displaystyle A z \bar{z} + \bar{E} z + E \bar{z} + D = 0$
Ahhhh! The light just went on. (So what if it's that little penguin that turns on the refrigerator light? I haven't had breakfast yet!)

Thank you.

-Dan

4. Originally Posted by topsquark
Ahhhh! The light just went on. (So what if it's that little penguin that turns on the refrigerator light? I haven't had breakfast yet!)

Thank you.

-Dan
Ha ha. You're welcome.

By the way, nostalgia ain't what it used to be