Chapter 4 Quadratic Functions and Factoring - 4.6 Perform Operations with Complex Numbers - 4.6 Exercises - Problem Solving - Page 281: 70

$c=i$ does belong to the Mandelbrot set.

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