Chapter 4 Quadratic Functions and Factoring - 4.6 Perform Operations with Complex Numbers - 4.6 Exercises - Problem Solving - Page 281: 72

$c=-1+i$ does belong to the Mandelbrot set.

Let $f (z)= z ^2 +(-1)$ $z_0=0$ $|z_0|=0$ $z_1=f(0)=0^2+(-1)=-1$ $|z_1|=1$ $z_2=f(-1)=(-1)^2+(-1)=0$ $|z_2|=0$ $z_3=f(0)=(0)^2+(-1)=-1$ $|z_3|=1$ $z_4=f(-1+3i)=(-1+3i)^2+(-1+i)=-9-5i$ $|z_4|=\sqrt 81+25=\sqrt 106$ $c=-1+i$ does belong to the Mandelbrot set.