# Graph of a Complex Number (basic concept)

1. Sep 11, 2009

### DEMJ

1. The problem statement, all variables and given/known data

Sketch $$0 \le arg z \le \frac{\pi}{4}$$ $$(z \not= 0)$$

3. The attempt at a solution

I know from my book that his is a punctured disk aka deleted neighborhood only because it says so and because it is in the form of $$0 < \mid z - z_0 \mid < \epsilon$$. I honestly have no clue how to graph this or even visual how it is a disk with a hole in it. Anyone care to mention or explain anything that will help me understand this concept and eventually be able to graph it. Thank you.

2. Sep 11, 2009

### Dick

It's not a punctured disk. If you can explain to me what you think arg(z) is, I think I can explain what the graph looks like. If you can explain that clearly, you probably won't need me to explain what the graph looks like.

3. Sep 11, 2009

### DEMJ

honestly I always think of it as the angle in radians you get when you graph a complex number z = x + iy but this may be wrong =[

4. Sep 11, 2009

### Dick

No, that's exactly right. So the region you are graphing should look more like a wedge, shouldn't it?

5. Sep 12, 2009

### DEMJ

I do not even know how to begin graphing this so I honestly do not see how it looks like a wedge...sigh.

All I can visualize is a vector z = x + iy with theta = pi/4 but this is cant be right and 0 must be involved somehow

Last edited: Sep 12, 2009
6. Sep 12, 2009

### Dick

Sigh. The set of points where arg(z)=0 is the positive x-axis, right? The set of points where arg(z)=pi/4 is a ray at 45 degrees to the x-axis, right? What you want are the points whose angles are in between. I would call that a "wedge". What would you call it?

7. Sep 12, 2009

### DEMJ

Wow I feel embarrassed how straight forward it is yet I could not grasp it by myself LOL, and I would call it Sergeant Dick Amazing (lol just kidding) and thank you for clearing this up for me kind sir.

8. Sep 12, 2009

### Dick

You'll do better next time, right? Not all 'complex' problems are hard.