# Complex number inequality graph

1. Apr 11, 2015

### Cpt Qwark

1. The problem statement, all variables and given/known data
How would Re(z)<0 be graphed?

2. Relevant equations
Re(z) is the real part of z

3. The attempt at a solution
It looks similar to y>x, but only shaded in the third quadrant, how can this be explained? not relevant anymore

Last edited: Apr 11, 2015
2. Apr 11, 2015

### robphy

Is there more to the problem?

Let z=x+iy, where x and y are real.
What is Re(z)?

3. Apr 11, 2015

### Cpt Qwark

The question doesn't tell, but let's just assume z=x+iy.

4. Apr 11, 2015

### haruspex

I'm not sure I understand. It should be half the plane.

5. Apr 11, 2015

### Cpt Qwark

I think i might be getting confused with the set notation,

if $$\alpha=\{z||x+iy|<n\}$$ and $$\beta=\{z|Re(z)>0\}$$, to graph $$\beta$$ would it just be the real part of $$\alpha?$$
$$\{x,y,n\} \in \mathbb{R}$$

6. Apr 11, 2015

### haruspex

Your definitions of alpha and beta are quite independent of each other, so why should there be any relationship between them?
Please post the question exactly as given.

7. Apr 11, 2015

### Cpt Qwark

take $$\alpha=\{z||e^{iπ/4}(z+2)|<2\}$$ $$(|e^{iπ}|=1)$$ and $$\beta=\{z|Re(z)>0\}$$,
how would beta be graphed?

8. Apr 11, 2015

### haruspex

That cannot be the whole question since the information about alpha is irrelevant.

9. Apr 11, 2015

### Cpt Qwark

sorry, forgot graph$$\alpha∩\beta$$

10. Apr 11, 2015

### haruspex

That makes a huge difference!
Ok, so what do you get for alpha and beta separately?
How would you combine the graphs to get the intersection?

11. Apr 11, 2015

### Cpt Qwark

I can graph alpha which is just $$|z+2]<2$$ but for beta is it just the real part of alpha?

12. Apr 11, 2015

### haruspex

No, the graph of beta has no connection with alpha. Why do you think it should? Forget alpha for the moment and figure out what beta looks like.
Or, did you mean to ask whether the intersection of the two is just the real part of alpha?

13. Apr 11, 2015

### Cpt Qwark

My original question was that i'm not sure how Re(z)>0 is graphed when there is no relation to alpha.

14. Apr 11, 2015

### haruspex

Ok. In the z=x+iy formulation, what does Re(z) look like in terms of x and y? What region of the complex plane does that correspond to?

15. Apr 11, 2015

### Cpt Qwark

Oh, ok I get it now.