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

question 128

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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=0.1+0.4iz = 0.1 + 0.4 i belong to the Mandelbrot set?

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Definitions:

Neuromuscular Junction

The synapse or junction where a motor neuron transmits a signal to a muscle fiber causing it to contract.

Muscle Fiber

An individual muscle cell, long and cylindrical, which contracts to produce movement.

Neurotransmitters

Chemicals released by neurons that transmit signals across a synapse from one neuron to another.

Skeletal Muscle

A type of muscle tissue that is attached to bones and is responsible for voluntary movements of the body.

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