complex number properties

• Apr 15th 2008, 05:53 AM
skystar
complex number properties
i made this example up...probably wont be nice solutions just want the general method.

|z-4|=3 and |z|=5 rt(10) how would i find where they intersect

i thought about substituting z=x+iy and finding x and y but im sure theres easier more general way?
• Apr 15th 2008, 06:00 AM
mr fantastic
Quote:

Originally Posted by skystar
i made this example up...probably wont be nice solutions just want the general method.

|z-4|=3 and |z|=5 rt(10) how would i find where they intersect

i thought about substituting z=x+iy and finding x and y but im sure theres easier more general way?

|z-4|=3 is a circle of radius 3 and centre at (4, 0).

|z|=5 rt(10) is a circle of radius 5 rt(10) and centre at (0, 0).

This lets you easily write down the Cartesian equation of each. Solve those equations simultaneously.

Off hand, I'd say the circles don't intersect ....
• Apr 15th 2008, 06:02 AM
skystar
tis what i thought i was just getting nasty roots for the real question i thought maybe there was a way of saying |z|=rt(zzbar) e.t.c thanks