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Math Help - Complex numbers again

  1. #31
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    Quote Originally Posted by ThePerfectHacker View Post

    Here is another hint: after you get the half-disk map the half-disk by (1-z)/(1+z).
    f_{1}(z) = z^{1/2} to get the half disc map
    f_{2}(z) = \frac{1-z}{1+z} this maps the half disc onto the 4th quadrant.
    f_{3}(z) = z^2 maps the 4th quadrant onto \Im(z) < 0
    f_{4}(z) = iz to rotate the region onto \Re(z) > 0
    f_{5}(z) = \frac{1-z}{1+z} maps the region onto the unit disc.

    f_5 \circ f_4 \circ f_3 \circ f_2 \circ f_1 = \frac{1 - i \left( \frac{1 - \sqrt{z}}{1+\sqrt{z}} \right)^2}{1 + i \left( \frac{1 - \sqrt{z}}{1+\sqrt{z}} \right)^2} I'm sure that can be simplified is it any good TPH?

    Bobak
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  2. #32
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    Quote Originally Posted by bobak View Post
    I'm sure that can be simplified is it any good TPH?
    That looks correct.

    I have ran out of lecture material, so we would have to end it here.
    Hopefully you now know some stuff about conformall mappings.
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