Streamlines from a complex potential

  • #1
Homework Statement:
Given a complex potential of the form $ ilog \frac{(z-a)}{ (z + a)} $, determine the current lines.
Relevant Equations:
${Psi = im(w)$
I've been trying this problem for a long time. By operating the lower part of the logarithm and clapping the real and imaginary part of the logarithm, I have come to the conclusion that the correct lines must be those in which it is true that:

$ d \ frac {(x ^ 2 + y ^ 2-a ^ 2) ^ 2 + 4y ^ 2a ^ 2} {(x + a (^ 2 + y ^ 2))}$

However, I am not able to operate this to get what kinds of curves it is.
 

Answers and Replies

  • #2
BvU
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complex potential of the form $$ \log \frac{(z-a)}{ (z + a)} $$, determine the current lines
Correct ? What is ##ilog## ?

You should preview your posts and fix things before posting.

In MathJax on PF, displayed math is enclosed in $$ and in-line math in ##

equally:
Relevant Equations: $${\Psi = im(w)}$$
backslash, uppercase Psi, curly right brace missing
And: what is ##w## ? And ##im## can be ##i## times ##m## or ##\operatorname {Im}##

I've been trying this problem for a long time. By operating the lower part of the logarithm and clapping the real and imaginary part of the logarithm
Instead of describing what you did, please post what you did. Not everybody understands what you do when you use the term 'clapping' ?
I have come to the conclusion that the correct lines must be those in which it is true that:
$$ d \frac {(x ^ 2 + y ^ 2-a ^ 2) ^ 2 + 4y ^ 2a ^ 2} {(x + a (^ 2 + y ^ 2))}$$
Help us to understand this conclusion.
However, I am not able to operate this to get what kinds of curves it is.
You could make a plot .. :rolleyes:

Ah, I see this was posted on April 1 :cool: --- any comment to add ?

[edit]for completeness: I'm not a native english speaker either.
 

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