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# Select the true statement about iterations of x2 + c = f(x) when x0 = 1 + i. and c = -i.

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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.

Dec 5, 2014

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Dec 5, 2014

#1
+27374
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Alan Dec 5, 2014
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I don't understand Alan

Dec 6, 2014
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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

Dec 6, 2014
#4
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The question mentions interations so I suppose this is the correct interpretation

BUT

where does it say in the question that       \$\$x_n=f(x_{(n-1)})\$\$

all I see is that   \$\$f(x)=x^2-i\$\$

I can certainly see that  \$\$x_0=1+i\$\$

I am completely unfamiliar with this wording (notation).

Dec 6, 2014