Results 1 to 8 of 8

Math Help - Complex Limit

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Complex Limit

    \lim_{z\rightarrow -i}\frac{z^4-1}{z+ i}

    What do I do with a Complex limit when I get \frac{0}{0}\mbox{?}
    Last edited by mr fantastic; November 6th 2010 at 01:08 PM. Reason: Fixed by applying common sense.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by dwsmith View Post
    \lim_{z\rightarrow -i}\frac{z^4-1}{z+ i}

    What do I do with a Complex limit when I get \frac{0}{0}\mbox{?}
    We want

    \displaystyle \lim_{z \to -i}\frac{z^4-1}{z+i}=\lim_{z \to -i}\frac{(z^2-1)(z^2+1)}{z+1}=\lim_{z \to -i}\frac{(z^2-1)(z+i)(z-i)}{z+i}=...
    Last edited by mr fantastic; November 6th 2010 at 01:09 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    sorry as a side note I also saw the Hebrew chars, but I don't think latex needs the tag mathbb for i. I also just use the letter i, but then again maybe i am lazy.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    I use the mathbb to bold the i.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1585
    Awards
    1
    Quote Originally Posted by dwsmith View Post
    I use the mathbb to bold the i.
    mathbb stands for 'math blackboard', not bold.
    [tex]\mathbb{Z}[/tex] gives \mathbb{Z}

    [tex]\boldmath{i}[/tex] gives \boldmath{i}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dwsmith View Post
    I use the mathbb to bold the i.
    If there is a problem using latex, common sense should be used to work around the problem. In this case, common sense dictates to just type i (which is what I did in my edit to the original post).
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by Plato View Post
    mathbb stands for 'math blackboard', not bold.
    [tex]\mathbb{Z}[/tex] gives \mathbb{Z}

    [tex]\boldmath{i}[/tex] gives \boldmath{i}
    My mistake \mathbf{} bolds the letters
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,522
    Thanks
    1405
    Quote Originally Posted by dwsmith View Post
    \lim_{z\rightarrow -i}\frac{z^4-1}{z+ i}

    What do I do with a Complex limit when I get \frac{0}{0}\mbox{?}
    You can also use L'Hospital's Rule.

    \displaystyle \lim_{z \to -i}\frac{z^4 - 1}{z + 1} = \lim_{z \to -i}\frac{\frac{d}{dz}(z^4 - 1)}{\frac{d}{dz}(z + 1)}

    \displaystyle = \lim_{z \to -i}\frac{4z^3}{1}

    \displaystyle = \lim_{z \to -i}{4z^3}

    \displaystyle = 4(-i)^3

    \displaystyle = 4i.


    This is also what you would get if you had factorised and cancelled the common factor of \displaystyle z+i.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Complex Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 18th 2010, 07:01 PM
  2. [SOLVED] Complex Limit (2)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 5th 2010, 08:17 PM
  3. complex limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 22nd 2009, 10:21 AM
  4. complex limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 25th 2008, 09:59 AM
  5. Replies: 1
    Last Post: March 3rd 2008, 07:17 AM

/mathhelpforum @mathhelpforum