# Complex number, region

• Oct 28th 2006, 09:29 PM
scorpion007
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.
• Oct 28th 2006, 10:27 PM
CaptainBlack
Quote:

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
• Oct 28th 2006, 11:29 PM
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 ?
• Oct 28th 2006, 11:49 PM
CaptainBlack
Quote:

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