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    The transformation T from the complex z-plane to the complex w-plane is given by

    w = z + 1
    . ------
    . z + i


    show that T maps points on the half-line arg(z) = pi/4 in the z-plane into points on the circle w = l 1 l in the w-plane.

    The mark scheme states that:

    z = λ + λ i

    w = ( λ + 1 ) + λ i
    . ----------------
    . λ + ( λ + 1 ) i

    l ( λ + 1 ) + λ i l = l λ + ( λ + 1 ) i l = √[ ( λ + 1 )² + λ²]



    I don't understand the last step, can anyone explain please?

    Thanks
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    |x + iy| =√(x² + y²)
    |y + ix| = √(y² + x²)
    :. |x + iy| = |y + ix| =√(x² + y²)

    simply replace x with (λ+1) and y with λ to get the MS explanation
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    arrghh..... thanks very much............
 
 
 
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Updated: June 25, 2005
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