Graph inequality in complex plane; negative z value

In summary, an inequality graph in the complex plane is a graphical representation of a mathematical inequality involving complex numbers. It displays the solutions to the inequality on a coordinate plane, with the real numbers on the horizontal axis and the imaginary numbers on the vertical axis. To graph an inequality in the complex plane, it must be rewritten in the standard form of <em>x + yi > b</em>, where <em>x</em> and <em>y</em> are real numbers and <em>i</em> is the imaginary unit. A negative z value in the graph indicates that the solution lies in the lower half of the complex plane. An inequality graph in the complex plane can have multiple solutions, as it is two-dimensional. It can
  • #1
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Homework Statement



Graph the following inequality in the complex plane: |1 - z| < 1

2. The attempt at a solution

In order to graph the inequality I need to get the left side in the form |z - ...|

|1 - z| < 1

|(-1)z + 1| < 1

|-1(z - 1)| < 1

|-1||z - 1| < 1

(1)|z - 1| < 1

|z - 1| < 1


From here I know how to graph it, but I'm not sure if my procedure is correct. Does this look right?
 
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  • #2
Sure it's correct. |a-b|=|b-a|. The proof is just what you showed. And they are both the distance from a to b.
 
  • #3
Thanks, didn't notice that.
 

1. What is an inequality graph in the complex plane?

An inequality graph in the complex plane is a graphical representation of a mathematical inequality involving complex numbers. It shows the solutions to the inequality on a coordinate plane with the real numbers on the horizontal axis and the imaginary numbers on the vertical axis.

2. How do you graph an inequality in the complex plane?

To graph an inequality in the complex plane, you first need to rewrite the inequality in the standard form of x + yi > b, where x and y are real numbers and i is the imaginary unit. Then, plot the boundary line and shade the region that satisfies the inequality.

3. What does a negative z value mean in an inequality graph in the complex plane?

A negative z value in an inequality graph in the complex plane means that the solution to the inequality lies in the lower half of the complex plane, below the x-axis. This is because the negative z values represent the negative imaginary numbers.

4. Can an inequality graph in the complex plane have multiple solutions?

Yes, an inequality graph in the complex plane can have multiple solutions. This is because the complex plane is two-dimensional, and the solutions to an inequality can be represented as a region on the plane rather than just a single point.

5. How can an inequality graph in the complex plane be useful in real-world applications?

An inequality graph in the complex plane can be useful in real-world applications such as economics, physics, and engineering. It can help visualize and analyze complex systems and relationships, such as supply and demand curves, electrical circuits, and fluid dynamics. It can also be used to solve optimization problems and make predictions about future outcomes.

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