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Complex Parametric Function

  • Thread starter Niles
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  • #1
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Homework Statement


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.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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925

Homework Statement


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.
For [itex]0\le t\le 1[/itex], yes. For [itex]1< t\le 2[/itex], x= t, y= 1. Draw those two pieces.
 
  • #3
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0
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.
 
  • #4
1,868
0
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:

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