# LaTeX - Practice 7-10-10

• Jul 10th 2010, 07:57 PM
DeanSchlarbaum
LaTeX - Practice 7-10-10

Division w. Complex Number Involvement --

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

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

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

$\displaystyle (8i)(4+3i) = 32i-24$

$\displaystyle \dfrac{32i-24}{25}$

Standard Form: $\displaystyle -\dfrac{24}{25}+\dfrac{32}{25}i$
• Jul 10th 2010, 11:49 PM
CaptainBlack
You will get big (displaystyle) fractions if you use \dfrac rather than frac:

$\displaystyle \frac{x+y}{z}$

$\displaystyle \dfrac{x+y}{z}$

CB
• Jul 12th 2010, 09:09 AM
DeanSchlarbaum
Quote:

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

$\displaystyle \frac{x+y}{z}$

$\displaystyle \dfrac{x+y}{z}$

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.)
• Jul 13th 2010, 10:55 AM
novice
You can practive here:
Online LaTeX Equation Editor
• Jul 13th 2010, 01:19 PM
CaptainBlack
Quote:

Originally Posted by DeanSchlarbaum

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
• Jul 13th 2010, 07:18 PM
DeanSchlarbaum
Quote:

Originally Posted by novice
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.
• Jul 13th 2010, 07:23 PM
DeanSchlarbaum
Quote:

Originally Posted by CaptainBlack
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.
• Jul 13th 2010, 07:24 PM
CaptainBlack
Quote:

Originally Posted by DeanSchlarbaum
[B]

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

One of the things you should know without thinking is that for any complex number $\displaystyle z=x+iy$ (with $\displaystyle $$x and \displaystyle$$ y$ real):

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

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:

$\displaystyle x^2+y^2=x^2-(iy)^2=(x+iy)(x-iy)$

CB