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Math Help - Complex Transformation

  1. #1
    Super Member craig's Avatar
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    Complex Transformation

    Hi again, just a quick question about a transformation in the complex plane.

    Here's the question:

    The transformation T from the complex z plane to the complex w plane is given by w = \frac{z+1}{z+i}.

    Show that T maps points on the half line arg{z} = \frac{\pi}{4} into points on the circle |w| = 1 in the w plane.

    The way I did this is by |\frac{z+1}{z+i}| = 1, leading to |z+1| = |z+i|.

    Now if we map the loci of these points we get the half line arg{z} = \frac{\pi}{4}.

    Just a few questions, firstly is this right? Is it ok to do it this way, instead of starting with the arg{z} = \frac{\pi}{4}, and is there another way to do this?

    Thanks in advance for the help
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  2. #2
    Super Member craig's Avatar
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    Anyone any ideas?
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