Question

Find the first four iterates of the function f(z)=z²-2-2i with an initial value of z base 0 = 2i?

Answer 1

To find the first four iterates of the function f(z)=z²-2-2i with an initial value of z base 0 = 2i, you can plug the initial value into the function and repeat the process for the resulting values.

Step-by-step explanation:

To find the first four iterates of the function f(z)=z²-2-2i with an initial value of z0 = 2i, we can use the following steps:

1. Let's start with z0 = 2i. Plugging this into the function, we have f(z0) = (2i)² - 2 - 2i = -2 - 4i.
2. Next, we can plug the result back into the function to find f(f(z0)). So f(f(z0)) = (-2 - 4i)² - 2 - 2i = -14 - 4i.
3. Similarly, we can find f(f(f(z0))) by plugging -14 - 4i back into the function. This gives us f(f(f(z0))) = (-14 - 4i)² - 2 - 2i = -198 - 104i.
4. Finally, we can find f(f(f(f(z0)))) by plugging -198 - 104i back into the function. This gives us f(f(f(f(z0)))) = (-198 - 104i)² - 2 - 2i = -38490 - 41776i.