# Mandelbrot set: knowing if a regular point is in the mandelbrot set

Let's say we have a point on an XY coordinate plane: $$A(0.2, -0.1)$$ We need to find if it's located in the mandelbrot set using the equation $$z'=z²+c$$ which means turning point A into a complex number.

I'm having trouble understanding the complicated symbols Wikipedia provides so I need help with turning points into complex numbers and using them in the equation.

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Your point is $$A=\left(\frac{1}{5},-\frac{1}{10}\right).$$ We can express it as $$a+ib$$: $$A=\frac{1}{10}\left(2-i\right).$$ Define the function $$f(z):=z^2+A.$$ Your point will belong to the Mandelbrot set if the sequence $$f(0),f(f(0)),f(f(f(0))),\ldots$$ remains bounded.
This will be the case since $$|A|=\sqrt{5}/10<2$$ and the disk centered at $$0$$ with radius $$2$$ belongs to the Mandelbrot set.
• I just factored the $1/10$. 2 days ago