Solve.
-A complex number $\mathrm { z }$ 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 $z = 0.7$ belong to the Mandelbrot set?
A) Yes
B) No

Question

Quizplus · Accepted Answer

For $z = 0.7$, the sequence starts with $0.7$, and the next term is $0.7^2 + 0.7 = 0.49 + 0.7 = 1.19$. Each subsequent term is calculated by squaring the previous term and adding 0.7. Since the modulus of these initial terms does not exceed 2, and considering the nature of the sequence, it's unlikely for the modulus to exceed 2 in further iterations for this value of $z$. Therefore, $z = 0.7$ likely belongs to the Mandelbrot set.

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

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