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

question 348

Multiple Choice

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

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Definitions:

Compounding Interval

the frequency at which interest is added to the principal balance of a financial instrument, affecting how much interest accumulates over time.

Monthly Compounded

An interest calculation method where interest is added to the principal sum at the end of each month, accelerating the growth of the investment through more frequent compounding.

Nominal Rate

The stated interest rate on a financial product, not accounting for inflation or the compounding of interest.

Effective Rate

The actual interest rate on an investment or loan, accounting for the effect of compounding over a given period.