1 Attachment(s)

Image for the region under the transformation w=z^2

Hi there. I have to find the image under the transformation for the region given in the pic.

http://www.mathhelpforum.com/math-he...1&d=1321552043

So, I tried to analyze what would happend. I know that:

And I've tried to express the region under consideration, I did it this way, I'm not pretty sure if this is right.

Then I should get

But doesn't give enough information to get the image under the transformation. So then I've tried to get the image for the lines.

Which gives something like semi infinite lines in w, right? but that would be wrong having in mind the limitations for the modulus in w.

And I don't know how to trasnform the other line, y=1-x.

1 Attachment(s)

Re: Image for the region under the transformation w=z^2

I would do this a little bit differently.

First let

Then

This gives that

Now you can just parameterize each of the line segments.

The vertical line segment from (1,0) to (1,1) is given by

Under the transformation this gives

so the start and end points are (1,0) and (0,2) now if you elminate the paramter you get the curve

So this is a parabolic arc.

Now for the horizontal line segemtn from (1,1) to (0,1) we have

under the transformation this gives

If you eliminate the parameter you get

we get another parabolic region with start point (0,1) and end point (-1,0)

Finally the line can be paramterized by

under the transformation this gives

If we eliminate the parameter we get

another parabola with start point (-1,0) and end point (1,0)

Here is a plot of the transformation. The first curve is in green, the 2nd in red, and the last in blue.

Re: Image for the region under the transformation w=z^2

Nice. Thank you verymuch :)