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Math Help - LaTeX - Practice 7-10-10

  1. #1
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    Lightbulb LaTeX - Practice 7-10-10

    Note: Please reply to this post with any helpful suggestions regarding LaTeX and/or to correct any mathematical error(s) I made.

    Division w. Complex Number Involvement --

    \dfrac{8i}{4-3i}

    \dfrac{8i}{4-3i} \times \dfrac{4+3i}{4+3i}

    (4-3i)(4+3i) = 16+12i-12i-9(i^2) = 16+12i-12i-9(-1) = 16+9 = 25

    (8i)(4+3i) = 32i-24

    \dfrac{32i-24}{25}

    Standard Form: -\dfrac{24}{25}+\dfrac{32}{25}i
    Last edited by DeanSchlarbaum; July 13th 2010 at 07:33 PM.
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    Grand Panjandrum
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    You will get big (displaystyle) fractions if you use \dfrac rather than frac:

    \frac{x+y}{z}

    \dfrac{x+y}{z}

    CB
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    Quote Originally Posted by CaptainBlack View Post
    You will get big (displaystyle) fractions if you use \dfrac rather than frac:

    \frac{x+y}{z}

    \dfrac{x+y}{z}

    CB
    CB: Thank you very much for method to make fractions larger.

    I have question for you since you know rules of Forum far better than I and you are "MHF Moderator": I want to learn how to use LaTeX Equation Editor and need to practice a lot. Most of the time I cannot spend long periods practicing. So, like my "practice" post of 7/10/10, I most often will just be able to do a little bit of practice at a time. What I would like to do is start a new "practice post" for each date that I am able to go online and practice with LaTeX. For instance, if this evening I have the time to go online I would like to be able to title a new post "LateX - Practice 7-12-10." The reason for this is that I like to print what I have done and keep it on file. But, I am concerned that in practicing in this manner I will have a lot of small posts on the Forum that might, somehow, take up to much "space" on the Forum. I don't want to do anything "wrong" here, in the Forum, if at all possible.

    My question is this: Is it alright to practice as I have indicated in above paragraph? Or, is it against the Forum rules and/or etiquette to do it that way, where I might end up posting a lot but with each practice post being of relatively short length? Is there a "better" way to practice when one has limited duration of time at any one time? I would appreciate your guidence regarding this matter.

    (Note: I have edited my original post using the \dfrac command. And, I have also changed the position of the minus sign in the last formua entry to more accurately reflect the Standard Form.)
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  4. #4
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    You can practive here:
    Online LaTeX Equation Editor
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    Grand Panjandrum
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    Quote Originally Posted by DeanSchlarbaum View Post

    My question is this: Is it alright to practice as I have indicated in above paragraph? Or, is it against the Forum rules and/or etiquette to do it that way, where I might end up posting a lot but with each practice post being of relatively short length? Is there a "better" way to practice when one has limited duration of time at any one time? I would appreciate your guidence regarding this matter.
    This forum is for playing around with LaTeX, so it is OK to do what you propose (but do expect comments)

    CB
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    Quote Originally Posted by novice View Post
    You can practive here:
    Online LaTeX Equation Editor
    novice: As time permits, I am trying to review as many of the past posts as possible in the LaTeX Help Section. In doing so, I found "www.codecogs.com/latex/. . . ." and I have put it on my IE "Favorites" toolbar already. I also found several other Websites that I can go to, then download and print all of the LaTeX commands. Having a printed reference by my keyboard when I'm using LaTeX will be invaluable! But, thank you very much for taking the time to help a "newbie" -- new to MHF, new to LaTeX, and in (too) many ways, new to Mathematics.
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    This forum is for playing around with LaTeX, so it is OK to do what you propose (but do expect comments)

    CB
    CB: Than I shall. And, I will not put in that "Note" at the beginning of posts. After I did it, I realized it was superfluous (or is "stupid" a better term?!). In other words, I will "expect comments" -- and I will welcome them.
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by DeanSchlarbaum View Post
    [B]

    (4-3i)(4+3i) = 16+12i-12i-9(i^2) = 16+12i-12i-9(-1) = 16+9 = 25
    One of the things you should know without thinking is that for any complex number z=x+iy (with $$ x and $$ y real):

    z\overline{z}=\overline{z}z=x^2+y^2

    It is the reason you have multiplied top and bottom by the conjugate of the denominator (that is to move all the imaginaries to the numerator). Also when I say "know without thinking" I mean once you have seen the product expanded and simplified and the relationship to the difference of two squares pointed out you should always in future take the short cut:

    x^2+y^2=x^2-(iy)^2=(x+iy)(x-iy)

    CB
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