Question

"Find the first three output values of the fractal-generating function f(z) = z2 − 2 + 2i.

A. −2 + 2i, −2 − 6i, −34 + 26i
B. −2 + 2i, −2 + 6i, −34 − 26i
C. −2 + 2i, −2 − 6i, 478 − 1766i
D. −2 − 6i, −34 + 26i, 478 − 1766i"

Answer 1

The first three output values of the fractal-generating function f(z) = z² − 2 + 2i starting with z = -2 + 2i are -2 + 2i, -2 + 6i, and -34 - 26i, which corresponds to Option B in the list provided.

Step-by-step explanation:

The task here is to find the first three output values of a fractal-generating function f(z) = z² − 2 + 2i.

We will calculate each value step-by-step starting with an initial value of z which is typically 0 in this case, but since the options provided have different starting points, we'll compare these directly.

For the first iteration, we simply plug in the initial value of z, which seems to be −2 + 2i based on the options provided:

f(z) = (−2 + 2i)² − 2 + 2i

The result from this first iteration is used as the new value of z to find the second output:

This process is repeated to find the third output:

f(z) = (− 34 − 26i)² − 2 + 2i

Between the options provided, the one that matches the correct calculations of this function sequence is Option B: −2 + 2i, −2 + 6i, −34 − 26i.