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Thread: general form of lines and circles in complex plane

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    general form of lines and circles in complex plane

    Prove the equation of a line and a circle in complex plane has a general form of :



    where

    Hence, or otherwise, prove

    If are complex numbers

    which satisfies below condition:



    then they are locus of circles in complex plane.
    Last edited by Mahan1; 26 Feb 2017 at 7:54 PM.
    Mahan Ghobadi

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    Re: general form of lines and circles in complex plane

    Quote Originally Posted by Mahan1 View Post
    Prove the equation of a line and a circle in complex plane has a general form of :



    where

    Hence, or otherwise, prove

    If are complex numbers

    which satisfies below condition:



    then they are locus of circles in complex plane.
























    Mahan1 likes this.

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    Re: general form of lines and circles in complex plane

    Quote Originally Posted by Mahan1 View Post
    Prove the equation of a line and a circle in complex plane has a general form of :



    where

    Hence, or otherwise, prove

    If are complex numbers

    which satisfies below condition:



    then they are locus of circles in complex plane.













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    Re: general form of lines and circles in complex plane

    Quote Originally Posted by omegadot View Post
























    That proves the above equation is a general form of a circle, but the question says that it also is the form of a line in the complex plane.
    To just add on to your proof:

    1.prove the equation below represents a line in complex plane:



    the equation of the line in general is :



    in complex plane, that translates into:



    where





    multiply by i:



    for

    we get

    Last edited by Mahan1; 26 Feb 2017 at 8:07 PM.
    Mahan Ghobadi

    Maths Tutor- ESL (80)| 2 Unit maths (96)(2013) | 3 Unit maths (99)| 4 Unit maths(95)| Physics (88)| music1(93)

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    Re: general form of lines and circles in complex plane

    Quote Originally Posted by Mahan1 View Post
    That proves the above equation is a general form of a circle, but the question says that it also is the form of a line in the complex plane.
    To just add on to your proof:

    1.prove the equation below represents a line in complex plane:



    the equation of the line in general is :



    in complex plane, that translates into:



    where





    multiply by i:



    for

    we get


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