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-A Complex Number z\mathrm { z } Does Not Belong to the Mandelbrot Set If Any of Belong

question 384

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-A complex number z\mathrm { z } does not belong to the Mandelbrot set if any of the complex numbers in the sequence z,z2+z,(z2+z) 2+z,[(z2+z) 2+z}2+z,z , z ^ { 2 } + z , \left( z ^ { 2 } + z \right) ^ { 2 } + z , \left[ \left( z ^ { 2 } + z \right) ^ { 2 } + z \right\} ^ { 2 } + z , \ldots has modulus exceeding 2 . Does z=0.50.4i\mathrm { z } = 0.5 - 0.4 \mathrm { i } belong to the Mandelbrot set?

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