Results 1 to 5 of 5

Math Help - Plotting with complex numbers

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    4

    Plotting with complex numbers

    Hi, I'm trying to plot a function like (2/3)Z + 1/(3Z^2), where Z is complex.

    I understand the basic idea of Z^2 = (x+iy)*(x+iy)= x^2+ 2xyi - y^2 is represented as x^2 - y^2 in the real direction, and 2xy in the imaginary direction.

    For the function I'm concerned with, however, there does not seem to be a way to break it into real and complex directions.

    Please let me know if there needs to be further clarification.

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Plotting with complex numbers

    Quote Originally Posted by Aesun View Post
    Hi, I'm trying to plot a function like (2/3)Z + 1/(3Z^2), where Z is complex.

    I understand the basic idea of Z^2 = (x+iy)*(x+iy)= x^2+ 2xyi - y^2 is represented as x^2 - y^2 in the real direction, and 2xy in the imaginary direction.

    For the function I'm concerned with, however, there does not seem to be a way to break it into real and complex directions.

    Please let me know if there needs to be further clarification.

    Thank you!
    (2/3)Z + \frac{1}{3Z^2}=(2/3)Z + \frac{\overline{Z}^2}{3|Z|^2}

    Now split the right hand side into real and imaginary parts and plot.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    Posts
    4

    Re: Plotting with complex numbers

    CaptainBlack, thank you for your help! Unfortunately I still don't see how to continue. Would you mind showing me a few more algebraic steps? I still can't seem to separate the real and imaginary parts.

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Plotting with complex numbers

    Quote Originally Posted by Aesun View Post
    CaptainBlack, thank you for your help! Unfortunately I still don't see how to continue. Would you mind showing me a few more algebraic steps? I still can't seem to separate the real and imaginary parts.

    Thank you!
    (2/3)Z + \frac{1}{3Z^2}=(2/3)Z + \frac{\overline{Z}^2}{3|Z|^2}

    Put:

     Z=x+iy

    then:

    \overline{Z}=x-iy

    and:

    \overline{Z}^2=x^2-2ixy-y^2=(x^2-y^2)-2ixy

    and:

    |Z|^2 = x^2+y^2

    Hence:

    (2/3)Z + \frac{1}{3Z^2}=(2/3)Z + \frac{\overline{Z}^2}{3|Z|^2} \\ \\ \\ \phantom{SSSSS}=\left[(2/3)x+\frac{x^2-y^2}{3(x^2+y^2)}\right]+\left[(2/3)y-\frac{2xy}{3(x^2+y^2)}\right]i

    Now check the algebra for mistakes.

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2011
    Posts
    4

    Re: Plotting with complex numbers

    Thank you so much! I'm new to working with complex numbers, so this was extremely helpful.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Plotting numbers in the complex plane?
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 5th 2011, 09:21 PM
  2. Replies: 2
    Last Post: March 25th 2011, 04:17 AM
  3. Complex Analysis, Plotting basic stuff
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 25th 2009, 08:13 AM
  4. Replies: 1
    Last Post: May 24th 2007, 04:49 AM
  5. Plotting Complex Variables on Argand Diagrams
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 8th 2006, 12:04 PM

Search Tags


/mathhelpforum @mathhelpforum