## Trigonometry (11th Edition) Clone

The point $~~1-1~i~~$ is not in the Mandelbrot set.
$z = 1-1~i$ We can perform the calculation $z^2+z$: $z^2+z = (1-1~i)^2+(1-1~i)$ $z^2+z = (0-2~i)+(1-1~i)$ $z^2+z = 1-3~i$ We can perform the calculation $(z^2+z)^2+z$: $z^2+z = (1-3~i)^2+(1-1~i)$ $z^2+z = (-8-6~i)+(1-1~i)$ $z^2+z = -7-7~i$ The absolute value is $\sqrt{(-7)^2+(-7)^2} = \sqrt{98}$ which is greater than 2. Therefore, the point $~~1-1~i~~$ is not in the Mandelbrot set.