Help me with Argand diagram

**rednest** · June 18th 2008, 11:35 PM

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 $|z-1| + |z-4| = 5$ .

**mr fantastic** · June 19th 2008, 01:52 AM

Originally Posted by rednest

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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