# Real Slice of Mandelbrot set

• Sep 1st 2012, 07:53 AM
klw289
Real Slice of Mandelbrot set
I'm trying to prove that the real slice of a Mandelbrot set is M n R =[-2,1/4]

I've tried researching it on the internet but everything I find seems to just state this and not prove it.
The hint I've been given to start is is to let

$c\in$(1/4, $\infty$) proving that for each $z\inR$ that $f_{\text{c}}(z)-z \geq c -$1/4

where $f_{\text{c}}(z)= z^2+c$

Any help would be greatly appreciated
• Sep 1st 2012, 11:36 AM
HallsofIvy
Re: Real Slice of Mandelbrot set
What you have written makes no sense. For any real number c, fc(z)- z is a complex number. You cannot say it is "larger than c- 1/4, a real number.

Perhaps you meant $\left|f_c(z)- z\right|\ge c- \frac{1}{4}$?