Hi

Show that in an Argand diagram the equation

$\displaystyle arg(z-2) - arg(z-2i) = \frac{3\pi}{4}$

represents an arc of a circle and that $\displaystyle |\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 $\displaystyle |z-1| + |z-4| = 5$.