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Math Help - Help me with Argand diagram

  1. #1
    Junior Member rednest's Avatar
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    Help me with Argand diagram

    Hi

    Show that in an Argand diagram the equation
    arg(z-2) - arg(z-2i) = \frac{3\pi}{4}
    represents an arc of a circle and that |\frac{z-4}{z-1}| is constant on this circle.
    Find the values of z corresponding to the points in which this circle is cut by the curve given by |z-1| + |z-4| = 5.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by rednest View Post
    Hi

    Show that in an Argand diagram the equation
    arg(z-2) - arg(z-2i) = \frac{3\pi}{4}
    represents an arc of a circle and that |\frac{z-4}{z-1}| is constant on this circle.
    Find the values of z corresponding to the points in which this circle is cut by the curve given by |z-1| + |z-4| = 5.
    This very question is discussed at length in this quite old thread started by bobak: http://www.mathhelpforum.com/math-he...lex-plane.html
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