Thread: How to Sketch The following Complex Eqn.

1. How to Sketch The following Complex Eqn.

pi/4 < Arg[z-(1-i)] < 3pi /4

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

Sketch

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

and interpret geometrically the difference

$\displaystyle w=z-(1-i)$

3. Originally Posted by saykhong
pi/4 < Arg[z-(1-i)] < 3pi /4
Note that geometrically $\displaystyle Arg(z - z_1) = \theta$ defines a ray with terminus at z = z1 (this point is not included however) and in the direction (anti-clockwise) of $\displaystyle \theta$ relative to a line parallel to the real axis passing through the terminus.