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complex variable?

Posted: Sat Apr 13, 2013 12:37 am
by hadimotamedi
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

Re: complex variable?

Posted: Sun Apr 14, 2013 1:57 pm
by redcar777
Its the intersection of a ellipse and a circle... does that help?

Re: complex variable?

Posted: Mon Apr 15, 2013 1:04 am
by hadimotamedi
Thank you for your reply. Can you please provide more details ?

Re: complex variable?

Posted: Mon Apr 15, 2013 2:29 am
by hadimotamedi
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 ?