Solve.
-A complex number $z$ does not belong to the Mandelbrot set if any of the complex numbers in the sequence $z , z ^ { 2 } + z , \left( z ^ { 2 } + z \right) ^ { 2 } + z , \left[ \left( z ^ { 2 } + z \right) ^ { 2 } + z \right] ^ { 2 } + z , \ldots$ has modulus exceeding 2. Does $z = - 1.4 i$ belong to the Mandelbrot set?
A) Yes
B) No

Question

Quizplus · Accepted Answer

The Mandelbrot set is defined for complex numbers $z$ for which the sequence $z, z^2 + z, (z^2 + z)^2 + z, \ldots$ does not diverge to infinity. A complex number does not belong to the Mandelbrot set if the modulus of any term in the sequence exceeds 2. For $z = -1.4i$, the first term is $z = -1.4i$, which has a modulus of $1.4$. The second term is $z^2 + z = (-1.4i)^2 - 1.4i = -1.96 - 1.4i$, which has a modulus greater than 2. Therefore, $z = -1.4i$ does not belong to the Mandelbrot set.

Solve -A Complex Number zzz Does Not Belong to the Mandelbrot Set If Any of Mandelbrot

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-A Complex Number $z$ Does Not Belong to the Mandelbrot Set If Any of Mandelbrot