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Math Help - Mathematical methods - Conformal mapping Q

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    Mathematical methods - Conformal mapping Q

    Hi, im really stuck on this question, Thankyou for any help in advance.

    4) i) For the line segment Lz and the semi-circle Cz
    Lz = {x, y : x = ln r, 0 < y < pi}
    Cz = {r, θ : r ∈ R+, 0 < θ < pi},
    show that the function

    f1(z) = ez

    maps Lz onto Cz.

    ii) Determine the length of the major and minor axis of the ellipse onto which the
    function
    f2(z) = z +(1/z)

    maps the semi-circle Cz.

    iii) Construct a conformal map that maps the line segment
    L′z = {x, y : x =pi/4, 0 < y < pi} onto an ellipse centered at the origin with major axis length
    a = 4 cosh pi/4 and minor axis length b = 4 sinh pi/4.

    The attachment is easier to read Q
    Attached Thumbnails Attached Thumbnails Mathematical methods - Conformal mapping Q-picture-1.png  
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