# Help me with Argand diagram

• Jun 18th 2008, 11:35 PM
rednest
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 $|z-1| + |z-4| = 5$.
• Jun 19th 2008, 01:52 AM
mr fantastic
Quote:

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