Determining graphical set of solutions for complex numbers

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1. Jan 4, 2017

TheChemist_

1. The problem statement, all variables and given/known data
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:

2. Relevant equations
|(z+i)/z| < 1

3. 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

2. Jan 4, 2017

Ray Vickson

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

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

3. Jan 4, 2017

Staff: Mentor

https://www.geogebra.org/

4. Jan 4, 2017

TheChemist_

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...

5. Jan 4, 2017

TheChemist_

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

6. Jan 4, 2017

Staff: Mentor

|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: Jan 5, 2017
7. Jan 5, 2017

TheChemist_

Ok thx guys I managed to solve it!

8. Jan 5, 2017

Staff: Mentor

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