# How to Sketch The following Complex Eqn.

• May 1st 2011, 11:52 PM
saykhong
How to Sketch The following Complex Eqn.
pi/4 < Arg[z-(1-i)] < 3pi /4
• May 2nd 2011, 12:27 AM
FernandoRevilla
Quote:

Originally Posted by saykhong
pi/4 < Arg[z-(1-i)] < 3pi /4

Sketch

$\pi/4<\textrm{Arg}\;(w)<3\pi/4$

and interpret geometrically the difference

$w=z-(1-i)$
• May 2nd 2011, 01:16 AM
mr fantastic
Quote:

Originally Posted by saykhong
pi/4 < Arg[z-(1-i)] < 3pi /4

Note that geometrically $Arg(z - z_1) = \theta$ defines a ray with terminus at z = z1 (this point is not included however) and in the direction (anti-clockwise) of $\theta$ relative to a line parallel to the real axis passing through the terminus.