Find the first three iterates of the function f(z)= z^2+2+i for the initial value of z0=3+3i.
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Find the first three iterates of the function f(z)= z^2+2+i for the initial value of z0=3+3i.

[From: ] [author: ] [Date: 12-04-21] [Hit: ]
I used WolframAlpha to do z2 and z3 (and to check z1).http://www.wolframalpha.com/input/?To compute z2 I just replaced 3+3i with 2+19i in the question bar and re-submitted the problem. Similarly for z3.......
Find the first three iterates of the function f(z)= z^2+2+i for the initial value of z0=3+3i. Thanks exaplain answer if you can.

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z1 = f(z0) = (3+3i)² + 2+i = (9 + 18i + (3i)²) + (2+i) = 2 + 19i
z2 = f(z1) = -355 + 77i
z3 = f(z2) = 120098 - 54669i

I used WolframAlpha to do z2 and z3 (and to check z1). A URL that will calculate z1 is

http://www.wolframalpha.com/input/?i=sim…

To compute z2 I just replaced "3+3i" with "2+19i" in the question bar and re-submitted the problem. Similarly for z3.
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