Select the true statement about iterations of x2 + c = f(x) when x0 = 1 + i. and c = -i.
A)The graph of the function's iterates shows no orbit.
B)The second iterate is f(x1) = 2i.
C)The first iterate is f(x1) = 2i.
D)The iterates repeat every two iterations.
Melody....we're just putting x0 = 1 + i into x2 + c and evaluating that, first...
So we have
(1 + i)2 + (-i) = (1 + 2i - i2) - i = ( 1 + 2i - 1) - i = i = x1
Then, we're putting this result back into x2 + c to get x2 =
(i)2 - i = -1 - i .......then we put this back into x2 + c to get x3
So on and so forth......and as Alan notes.....it sets up a repeating "2 cycle" pattern