Complex number inequality graph

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

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robphy
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Is there more to the problem?

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

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

haruspex
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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.

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
Homework Helper
Gold Member
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.

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

haruspex
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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.

That cannot be the whole question since the information about alpha is irrelevant.
sorry, forgot graph$$\alpha∩\beta$$

haruspex
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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?

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
Homework Helper
Gold Member
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?

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