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

A. 2 + i, 5 + 5i, - 2595 + 205i

B. 2 + i, 2 + 51i, - 2595 + 205i

C. 2 + i, 5 + 5i, 2 + 51i

D. 5 + 5i, 2 + 51i, - 2595 + 205i

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Answers (1)
  1. 7 June, 03:33
    0
    A fractal generating function is given by

    f (z) = Z² + 2 + i

    →f (0) = 0² + 2 + i

    = 2 + i

    →f (2+i) = (2+i) ² + 2 + i →Use identity (a+b) ² = a² + b² + 2 a b

    and i² = - 1

    = 4 + 4 i - 1 + 2 + i

    = 5 + 5 i

    Now→, f (5 + 5 i) = (5 + 5 i) ² + 2 + i →Use identity (a+b) ² = a² + b² + 2 ab

    and i² = - 1

    = 25 - 25 + 50 i + 2 + i

    = 51 i + 2

    →So, f (0) = 2 + i, f (2 + i) = f (5 + 5 i) = 2 + 51 i

    →Option C, 2 + i, 5 + 5 i, 2 + 51 i are the first three output of fractal generating function f (z) = z² + 2 + i.
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