Results 1 to 4 of 4

Math Help - The Complex Plane

  1. #1
    Junior Member
    Joined
    Nov 2007
    Posts
    28

    The Complex Plane

    Right now, I am learning of the Complex Plane, and I believe that I am having difficulty truly understanding what this means. So far, this is how I visualized it:

    you have:

    a + bi

    and these two parts of the complex number can be graphed on the complex plane, which is a variant of the cartesian plane with an x and y axis for real and imaginary numbers respectively.






    If you add two real numbers A and B, you get a value that is itself real because it's like taking an actual length and adding on another actual length.





    In this case, you are adding a real number a with an imaginary number bi, which can not be defined on a real number line. When you try to add these two guys together, it's quite unlike your first case because you cannot add these lengths together in a linear fashion. Therefore you have to represent imaginary numbers on a different line. your result for adding these two together is expressed as a + bi, which is the blue line.

    Is this the correct way of thinking about complex numbers and their graphing on the complex plane? If I am of or if there's something more to this concept that I need to visualize or understand, I would really like to know.

    Thanks
    ---Richard
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Skinner View Post
    Right now, I am learning of the Complex Plane, and I believe that I am having difficulty truly understanding what this means. So far, this is how I visualized it:

    you have:

    a + bi

    and these two parts of the complex number can be graphed on the complex plane, which is a variant of the cartesian plane with an x and y axis for real and imaginary numbers respectively.






    If you add two real numbers A and B, you get a value that is itself real because it's like taking an actual length and adding on another actual length.





    In this case, you are adding a real number a with an imaginary number bi, which can not be defined on a real number line. When you try to add these two guys together, it's quite unlike your first case because you cannot add these lengths together in a linear fashion. Therefore you have to represent imaginary numbers on a different line. your result for adding these two together is expressed as a + bi, which is the blue line.

    Is this the correct way of thinking about complex numbers and their graphing on the complex plane? If I am of or if there's something more to this concept that I need to visualize or understand, I would really like to know.

    Thanks
    ---Richard
    There is an Algebraic way of looking at the complex number system, but for most people's purposes you have the concept down nicely.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2007
    Posts
    28
    Oh yeah I know that there's the polar form of expressing complex numbers and such, but I was just making sure that I was making sense conceptually. my precal teacher told me that it was incorrect way of thinking about it but I don't really see where he's getting at anyway.

    Is there anything else I should know in algebraic terms that would really enrich my understanding of this topic? I don't want to leave anything about this topic in ambiguity, at least within my scope of learning at the moment.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    Quote Originally Posted by Skinner View Post
    Is there anything else I should know in algebraic terms that would really enrich my understanding of this topic? I don't want to leave anything about this topic in ambiguity, at least within my scope of learning at the moment.
    I agree with Dan that you seem to have a basic grasp of the concept.
    I do wonder how you are dealing with the multiplication of complex numbers?

    Just as we have the algebraic structure of a field for the real numbers, we must have that same structure on the complex numbers. So we must have additive and multiplicative identities. All numbers must have additive inverses all nonzero numbers must have multiplicative inverses. On that last point, it is important for you to under stand that the expression \frac{1}{{3 + 4i}} is not considered a proper complex number. Its correct form is \frac{1}{5} - \frac{4}{5}i. You may want to find out why that is the case.

    One finial point: I would encourage you to consider the number i as what it is.
    The number i is simply a number that solves the equation <br />
z^2  + 1 = 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: September 13th 2011, 08:16 AM
  2. Replies: 10
    Last Post: September 11th 2011, 01:06 AM
  3. Replies: 12
    Last Post: June 2nd 2010, 03:30 PM
  4. Euclidean plane vs the complex plane
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 16th 2010, 01:55 PM
  5. Replies: 2
    Last Post: December 3rd 2008, 07:26 PM

Search Tags


/mathhelpforum @mathhelpforum