Complex number inequality graph

[Cpt Qwark]

Homework Statement

How would Re(z)<0 be graphed?

Homework Equations

Re(z) is the real part of z

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

 

[robphy]

Is there more to the problem?

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

 

[Cpt Qwark]

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

 

[haruspex]

Homework Statement

How would Re(z)<0 be graphed?

Homework Equations

Re(z) is the real part of z

The Attempt at a Solution

It looks similar to y>x, but only shaded in the third quadrant, how can this be explained?

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

 

[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 $$\alpha?$$
$$\{x,y,n\} \in \mathbb{R}$$

 

[haruspex]

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 $$\alpha?$$
$$\{x,y\} \in \mathbb{R}$$

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.

 

[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?

 

[haruspex]

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

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

 

[Cpt Qwark]

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

sorry, forgot graph$$\alpha∩\beta$$

 

[haruspex]

sorry, forgot graph$$\alpha∩\beta$$

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?

 

[Cpt Qwark]

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?

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

 

[haruspex]

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

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?

 

[Cpt Qwark]

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?

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

 

[haruspex]

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

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?

 

[Cpt Qwark]

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?

Oh, ok I get it now.
Thanks for your help!