Determining graphical set of solutions for complex numbers

[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:

Homework Equations

|(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

 

[Ray Vickson]

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:

Homework Equations

|(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 $|z|$?

 

[jedishrfu]

Checkout Geogebra, its an educational software tool for students and it may be able to help you learn more about complex numbers.

https://www.geogebra.org/

 

[TheChemist_]

Checkout Geogebra, its an educational software tool for students and it may be able to help you learn more about complex numbers.

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...

 

[TheChemist_]

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...

 

[Mark44]

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.

 

[TheChemist_]

Ok thanks guys I managed to solve it!

 

[Mark44]

Typo:

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