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.
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.