Map of Area Bounded by y=5x & y=-3x in Upper Plane

[Amer]

what is the map of the area bound by y=5x and y=-3x in the upper half plane, under w=1/z we have the lines : $ z(t) = t + 5t i $ , and the line $z(t) = t - 3ti $
Fist line
$\displaystyle w_1 = \dfrac{1}{t+5ti} = \dfrac{1}{26t} - \dfrac{5i}{26t} $
Second
$\displaystyle w_2 = \dfrac{1}{t - 3ti} = \dfrac{1}{10t} + \dfrac{3i}{10t} $

We get the lines in the uv plane

$v = -5u \; , v=3u $
taking a point in the area for example (0,1) under 1/z (0,1) so we will take the bounded area between $v = -5u \; , v=3u $ which has the point (0,1)
is that right ?
Thanks

 

[Opalg]

You have correctly found the boundary lines as $v = -5u$ and $v=3u $. But if the original area in the $z$-plane contains the point $(0,1)$ then the image in the $w$-plane should contain the image of that point under the map $w=1/z$.