# Thread: LaTeX - Practice 7-10-10

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

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: $-\dfrac{24}{25}+\dfrac{32}{25}i$

2. You will get big (displaystyle) fractions if you use \dfrac rather than frac:

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

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

CB

3. Originally Posted by CaptainBlack
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.)

4. You can practive here:
Online LaTeX Equation Editor

5. 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

6. 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.

7. 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.

8. Originally Posted by DeanSchlarbaum
[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