# Thread: complex number properties

1. ## 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?

2. 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 ....

3. 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