![]() The coordinate system in the range is panned so that the origin is now in the center of the window. ![]() To recenter (pan) the range, double-click on the origin (0, 0) of the coordinate system in the range. If you move the mouse over the y-intercept on the range you can see that the y-intercepts of the right-most parabola are z = −8 i and z = +8 i, approximately. You should now see see the entire parabolas in the range. Then click on Okay (or Apply) You should now see that vertical lines are mapped to left-right parabolas, opening to the left To zoom out in the range, click Range zoom out twice. Also set the number of lines for the vertical lines to 2 (it does not matter how many horizontal lines you enter). Click on the Rectangle Options button A dialog window will appear where you can adjust the parameters or your lines Adjust the parameters so that the Horizontal Lines go from −10 to 10, while the Vertical Lines go from 1 to 2. You now see several vertical lines and their images, while the horizontal lines are no longer visible. The applet should appear, with two horizontal lines and their images visible Check the V-lines and uncheck the H-lines checkboxes. Into what curves does the complex function f( z) = z 2 transform vertical lines such as the vertical line through z = 2? Answerīefore we check the answer mathematically, we use ZMap to come up with a good guess: Start ZMap by clicking on the above applet button. You will see that both lines are mapped to "left-right" parabolas, as shown before. If you click the above example, the function f( z) = z 2 has been pre-selected, together with two horizontal lines through z = 1/2 i and z = i.
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