## complex variable?

Forum for the GRE subject test in mathematics.
hadimotamedi
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

### complex variable?

Dear All
In the following set of equations, two-equations one-complex variable :
abs(z+16) + abs(z) = 20
abs(z+8) = 7
Where abs stands for absolute value . The variable z is from the complex z-plane . How many solutions does this set of equations have ?
The answers are as :
1- Four distinct solutions
2- Three distinct solutions
3- Two distinct solutions
4- On solution
Which one is correct in your opinion ?
Thank you

redcar777
Posts: 34
Joined: Sun Nov 04, 2012 11:59 am

### Re: complex variable?

Its the intersection of a ellipse and a circle... does that help?

hadimotamedi
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

### Re: complex variable?

Thank you for your reply. Can you please provide more details ?

hadimotamedi
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

### Re: complex variable?

According to you, the first equation is an ellipse with focus at (-16,0) and (0,0) and 2a=20 and the second equation is a circle with center at (-8,0) and radius of 7 so they intersect at two points. It is correct in your opinion ?