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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.







Guest Dec 5, 2014

Best Answer 

 #1
avatar+26412 
+13

This might help you answer the question:

 recursion

.

Alan  Dec 5, 2014
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4+0 Answers

 #1
avatar+26412 
+13
Best Answer

This might help you answer the question:

 recursion

.

Alan  Dec 5, 2014
 #2
avatar+91510 
0

I don't understand Alan  

Melody  Dec 6, 2014
 #3
avatar+81135 
+5

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

 

CPhill  Dec 6, 2014
 #4
avatar+91510 
0

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).

Melody  Dec 6, 2014

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