Thread: Complex number, region

1. Complex number, region

Can someone please draw for me the shaded region represented by:

Arg(z) <= -5 PI/6

I'm having trouble visualizing. (note that -PI < Arg(z) <= PI)

I'm thinking its either the region from the positive Re(z) axis, clockwise to -5PI/6, or perhaps everything except the region from -5 PI/6 -> PI.

I'm not sure.

2. Originally Posted by scorpion007
Can someone please draw for me the shaded region represented by:

Arg(z) <= -5 PI/6

I'm having trouble visualizing. (note that -PI < Arg(z) <= PI)

I'm thinking its either the region from the positive Re(z) axis, clockwise to -5PI/6, or perhaps everything except the region from -5 PI/6 -> PI.

I'm not sure.
It is the second of these. Consider the a point z with Arg(z)=-5.5 pi/6,
this is in the region you want as:

-5.5 pi/6 < -5 pi/6.

While:

-4.5 pi/6 > -5 pi/6

and so is not in the required region.

RonL

3. ah thanks, i think i get it.

So that means Arg(z) <= -5/6 PI lies in the 3rd quadrant, and is the region from -5/6PI to -PI ?

4. Originally Posted by scorpion007
ah thanks, i think i get it.

So that means Arg(z) <= -5/6 PI lies in the 3rd quadrant, and is the region from -5/6PI to -PI ?
Yes.

RonL