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Math Help - sketching rotation of complex function.

  1. #1
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    complex function. (rotation)

    Hi,

    A function H(z) =e^(iθ)z generate a rotation mapping. Sketch the image of the semidisk |Z|<=2, Im Z <= 0 under H when

    a.θ= pi/4
    b.θ= -pi/4
    c.θ= 3pi/4

    ok, so basically my question for a. is, do i apply the constraints and draw the disk, then do the rotation, or do the constraints still apply after the rotation. If you look at what i have done in the attachment you will probably know what i'm asking, should the part shaded black with the '?' be included or not? Thanks.
    Attached Thumbnails Attached Thumbnails sketching rotation of complex function.-mathhelp.jpg  
    Last edited by linalg123; August 9th 2012 at 08:47 AM.
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  2. #2
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    Re: complex function. (rotation)

    You substitute in the  \theta first and then find the image of the region under H. There's no other way. Yes, the region with question mark is included. You're just rotating the region counterclockwise by \pi/4. Part (b) will be a clockwise rotation by \pi/4, etc.
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