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

question 153

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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=0.4iz = 0.4 i belong to the Mandelbrot set?


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