How do you draw on an argand diagram:
$\{z\in{\mathbb C}: \arg(z-1) < \arg(z-i)\}$?
I can plot both points but I don't know what to do with arguments and inequalities.
[Math] complex numbers – argand diagram
complex numbersgraphing-functions
complex numbersgraphing-functions
How do you draw on an argand diagram:
$\{z\in{\mathbb C}: \arg(z-1) < \arg(z-i)\}$?
I can plot both points but I don't know what to do with arguments and inequalities.
Best Answer
If you simply interpret what it means to say that $\arg(z-1)<\arg(z-i)$ geometrically, then it shouldn't be too hard to visualize the region. In each of the regions below, the argument of the point ($z$) minus the number (either $1$ or $i$) simply the angle from the dashed line to the arrow. It's easy to see that this angle is smaller from the complex number $1$ in exactly the blue regions.
Note that I'm assuming a branch cut at $\pi$ in the argument function so that, in the horizontal strip, $\arg(z-1)$ is definitely negative while $\arg(z-i)$ is positive.