<h3>Answer: 1+2i, -2+6i, -31-22i</h3>
===========================================
Work Shown:
Plug in z = 0 and c = 1+2i. Simplify.
f(z) = z^2 + c
f(0) = 0^2 + 1+2i
f(0) = 1+2i
The output 1+2i will be the input for the next iteration
--------------------
Plug in z = 1+2i. Keep c = 1+2i the same.
f(z) = z^2 + c
f(1+2i) = (1+2i)^2 + 1+2i
f(1+2i) = 1+4i+4i^2 + 1+2i
f(1+2i) = 1+4i+4(-1) + 1+2i
f(1+2i) = 1+4i-4 + 1+2i
f(1+2i) = -2+6i
The output -2+6i will be the input for the next iteration.
--------------------
Plug in z = -2+6i. Keep c = 1+2i the same.
f(z) = z^2 + c
f(-2+6i) = (-2+6i)^2 + 1+2i
f(-2+6i) = 4-24i+36i^2 + 1+2i
f(-2+6i) = 4-24i+36(-1) + 1+2i
f(-2+6i) = 4-24i-36 + 1+2i
f(-2+6i) = -31-22i
