Select the true statement about iterations of x^{2} + c = f(x) when x_{0} = 1 + i. and c = -i.

A)The graph of the function's iterates shows no orbit.

B)The second iterate is f(x_{1}) = 2i.

C)The first iterate is f(x_{1}) = 2i.

D)The iterates repeat every two iterations.

Guest Dec 5, 2014

#3**+5 **

Melody....we're just putting x_{0 }= 1 + i into x^{2} + c and evaluating that, first...

So we have

(1 + i)^{2} + (-i) = (1 + 2i - i^{2}) - i = ( 1 + 2i - 1) - i = i = x_{1}

Then, we're putting this result back into x^{2} + c to get x_{2} =

(i)^{2} - i = -1 - i .......then we put this back into x^{2} + c to get x_{3}

So on and so forth......and as Alan notes.....it sets up a repeating "2 cycle" pattern

CPhill
Dec 6, 2014