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Math Help - [SOLVED] Graph of a line in the Argand plane

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

    I am having a mental block about this.

    Given the equation
    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 A \neq 0, A and D real constants, E a complex constant, and E \bar{E} - AD > 0 this is supposed to represent a circle.)

    So using the condition I've got:
    \bar{E} z + D = 0

    Thus
    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
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  2. #2
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    Quote Originally Posted by topsquark View Post
    I am having a mental block about this.

    Given the equation
    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 A \neq 0, A and D real constants, E a complex constant, and E \bar{E} - AD > 0 this is supposed to represent a circle.)

    So using the condition I've got:
    \bar{E} z + D = 0

    Thus
    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:

    A z \bar{z} + \bar{E} z + E \bar{z} + D = 0
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Hi there topsquark.

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

    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
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  4. #4
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    Quote Originally Posted by topsquark View Post
    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
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