I'm not sure I understand. It should be half the plane.Cpt Qwark said: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?
Your definitions of alpha and beta are quite independent of each other, so why should there be any relationship between them?Cpt Qwark said:I think i might be getting confused with the set notation,
if [tex]\alpha=\{z||x+iy|<n\}[/tex] and [tex]\beta=\{z|Re(z)>0\}[/tex], to graph [tex]\beta[/tex] would it just be the real part of [tex]\alpha?[/tex]
[tex]\{x,y\} \in \mathbb{R}[/tex]
That cannot be the whole question since the information about alpha is irrelevant.Cpt Qwark said:take [tex]\alpha=\{z||e^{iπ/4}(z+2)|<2\}[/tex] [tex](|e^{iπ}|=1)[/tex] and [tex]\beta=\{z|Re(z)>0\}[/tex],
how would beta be graphed?
sorry, forgot graph[tex]\alpha∩\beta[/tex]haruspex said:That cannot be the whole question since the information about alpha is irrelevant.
That makes a huge difference!Cpt Qwark said:sorry, forgot graph[tex]\alpha∩\beta[/tex]
haruspex said: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?
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.Cpt Qwark said:I can graph alpha which is just [tex]|z+2]<2[/tex] but for beta is it just the real part of alpha?
haruspex said: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?
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 said:My original question was that I'm not sure how Re(z)>0 is graphed when there is no relation to alpha.
Oh, ok I get it now.haruspex said: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?
A complex number inequality graph is a visual representation of inequalities involving complex numbers. The graph is typically plotted on a complex plane, with real numbers on the x-axis and imaginary numbers on the y-axis.
To graph a complex number inequality, first plot the boundary line or curve of the inequality on the complex plane. Then, choose a test point not on the boundary and plug it into the inequality. If the inequality is true for that point, shade the region containing the point. If it is false, shade the region not containing the point.
The purpose of graphing complex number inequalities is to visually represent the solution set of the inequality. This can help in understanding the relationship between the complex numbers and identifying any patterns or trends.
To solve a system of complex number inequalities, graph each inequality on the same complex plane and determine the overlapping region. The solution set will be the intersection of the solution sets for each individual inequality.
Yes, complex number inequalities can have multiple solutions. The solution set may consist of individual points, regions, or even infinite solutions depending on the specific inequality.