Filled Julia set - check my solution if it is right.

[foxofdesert]

Homework Statement

Suppose f(z) = z^3 -27z + 15
Find R such that |f(z)|>|z| whenever |z|>R.

Homework Equations

The Attempt at a Solution

Let f(z)=z, then I have z^3 -28z + 15 = 0
then,

z=5, (-5+√(17))/2, (-5-√(17))/2.

since 5 is the most further point, R=5.

check my solution if it is right. I did it, but I am not so sure.

 

[lanedance]

so at z=5, f(5) = 0 and at z=5+e, for some small e>0, f will still be pretty small, so I don't think you've nailed it

you need to find where
|f(z)|-|z|>0