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Complex Parametric Function

  1. May 1, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    I am given the following parametric function in the complex plane C:

    [tex]
    \gamma = \left\{ {\begin{array}{*{20}c}
    {t^2 + it\,\,\,\,\,\,\,\,{\rm{for }}\,\,t \in [0,1]} \\
    {t + i\,\,\,\,\,\,\,\,\,\,\,\,{\rm{for }}\,\,t \in ]1,2]} \\
    \end{array}} \right.
    [/tex]

    In order to sketch it for t in [0,1], will it be correct it I set x(t) = t2 and y(t) = t, and sketch it in the real plane?

    Thanks in advance.

    Best regards,
    Niles.
     
  2. jcsd
  3. May 1, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    For [itex]0\le t\le 1[/itex], yes. For [itex]1< t\le 2[/itex], x= t, y= 1. Draw those two pieces.
     
  4. May 2, 2009 #3
    Thanks.

    Lets look at e.g. w = z2 = r2ei2K = r2(cos(2K) + isin(2K)), where K is the argument of z and r is the modulus. If I wish to plot w = z2, then can I do this by plotting x(t) = r2cos(2K) and y(t) = r2sin(2K) as well?

    Best regards,
    Niles.
     
  5. May 3, 2009 #4
    The reason why I am asking is that I seem to get confused when I look at complex numbers as mere parametric functions. Is it correct to look at them in this sense?
     
    Last edited: May 3, 2009
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