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Math Help - Limits with complex varibles.

  1. #1
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    Limits with complex varibles.

    I am having trouble with
    Limit of 2x+iy^2 as z->2i

    i set it up at lim 2x as x->0 + i lim y^2 as y->2. so i get 4i as my limit but when i plug 2i directly i get -4i... is this right because of how the complex plain is defined?? or am i completely wrong thinking the limit is 4i? any help would be awesome!
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    The first problem is that you have a function in terms of x and y, but telling it to make z go to a value.

    What is z?
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  3. #3
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    z = x+yi so w= 0+2i?

    i thought that i would do \displaystyle \lim_{z \to w}\2x+iy^2 = \lim_{\left(x,y\right) \to (0,2)} 2x + i \lim_{(x,y) \to (0,2)} y^2
    Last edited by fizzle45; September 16th 2010 at 06:17 PM.
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    If you are evaluating \lim_{(x, y) \to (0, 2)}(x + iy^2)...


    \lim_{(x, y) \to (0, 2)}(x + iy^2) = 0 + i(2^2)

     = 4i.
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  5. #5
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    Quote Originally Posted by fizzle45 View Post
    I am having trouble with
    Limit of 2x+iy^2 as z->2i

    i set it up at lim 2x as x->0 + i lim y^2 as y->2. so i get 4i as my limit but when i plug 2i directly i get -4i... is this right because of how the complex plain is defined?? or am i completely wrong thinking the limit is 4i? any help would be awesome!
    The errror is that you plugged 2i in for y. z= 2i, not y. Writing z= x+ iy then z= 2i means y= 2, not 2i.
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