# Determining graphical set of solutions for complex numbers

• TheChemist_
In summary, the conversation discusses a problem with solving an equation involving complex numbers and the attempt to graph the solutions on a coordinate system. The equation is rewritten to |z+i| < |z| and the graphical interpretations of |z+i| and |z| are explored using Geogebra. The conversation ends with the person successfully solving the problem.
TheChemist_

## Homework Statement

So we have been doing complex numbers for about 2 weeks and there is this one equation I just can't solve.
It's about showing the set of solutions in graphical form (on "coordinate" system with the imaginary and the real axis). So here is the equation:

|(z+i)/z| < 1

## The Attempt at a Solution

Well, I just don't know how to solve this "thing"
The only thing we did was to picture some other solutions...

I hope you can help me with this little problem!
Thx

TheChemist_ said:

## Homework Statement

So we have been doing complex numbers for about 2 weeks and there is this one equation I just can't solve.
It's about showing the set of solutions in graphical form (on "coordinate" system with the imaginary and the real axis). So here is the equation:

|(z+i)/z| < 1

## The Attempt at a Solution

Well, I just don't know how to solve this "thing"
The only thing we did was to picture some other solutions...

I hope you can help me with this little problem!
Thx

Write it as ##|z+i| < |z|##.

What are the graphical/geometric interpretations of the quantities ##|z+i|## and ##|z|##?

Mark44

https://www.geogebra.org/

jedishrfu said:

https://www.geogebra.org/

yeah I know geogebra and I use it quite often, but I haven't been able to figure out how I can view complex numbers...

Ray Vickson said:
Write it as ##|z+i| < |z|##.

What are the graphical/geometric interpretations of the quantities ##|z+i|## and ##|z|##?

Ok that made things a little clearer...but i still can't figure out how |z+i| could look...

TheChemist_ said:
Ok that made things a little clearer...but i still can't figure out how |z+i| could look...
|z + i| is the same as |z - (-i)|; i.e. the distance between a complex number z and the imaginary number -i. |z| represents the distance from the same z to the origin.
Edit: Fixed typo pointed out by SammyS.

Last edited:
Ok thanks guys I managed to solve it!

SammyS said:
Typo:
Thanks, SammyS. -i was what I meant. It's fixed in my earlier post now.

## What is the purpose of determining a graphical set of solutions for complex numbers?

The purpose of determining a graphical set of solutions for complex numbers is to visually represent the solutions to a complex equation or system of equations. This can help in understanding the behavior of complex numbers and their relationships with each other.

## How is a graphical set of solutions for complex numbers determined?

A graphical set of solutions for complex numbers is determined by plotting the complex numbers on a coordinate plane, with the real part of the number on the horizontal axis and the imaginary part on the vertical axis. The solutions are then represented as points on the plane.

## What are the different types of solutions that can be represented in a graphical set of solutions for complex numbers?

The different types of solutions that can be represented in a graphical set of solutions for complex numbers include real solutions, imaginary solutions, and complex solutions. Real solutions are represented as points on the horizontal axis, imaginary solutions are represented as points on the vertical axis, and complex solutions are represented as points in the plane.

## Can a graphical set of solutions for complex numbers have more than one solution?

Yes, a graphical set of solutions for complex numbers can have multiple solutions. This is because a complex equation or system of equations can have multiple solutions in the form of complex numbers. Each solution would be represented as a point on the coordinate plane.

## What are the benefits of using a graphical set of solutions for complex numbers?

Using a graphical set of solutions for complex numbers can help in visualizing and understanding the solutions to complex equations or systems of equations. It can also aid in identifying patterns and relationships between complex numbers, and can be a useful tool in problem-solving and making predictions.

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