Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.4 De Moivre's Theorem: Powers and Roots of Complex Numbers - 8.4 Exercises - Page 383: 51a

The point $0+0~i$ is in the Mandelbrot set.

$z = 0+0~i$ We can perform the calculation $z^2+z$: $z^2+z = (0+0~i)^2+(0+0~i)$ $z^2+z = (0+0~i)+(0+0~i)$ $z^2+z = 0+0~i$ If we perform this calculation repeatedly, we will get the same result and the absolute value is not greater than 2. Therefore, the point $0+0~i$ is in the Mandelbrot set.