Question

Find the first three iterates of the function f(z)=z2+c with a value of c=1+2i and an initial value of z0=0

Answer 1

14x

Explanation:

multiply the 2i by the 0 eulogistic quotient

Answer 2

z1 = 1+2i

z2 = -2 + 6i

z3 = -31 - 22i

Explanation:

Given that: z(n+1) = z(n)² + c, c = 1+2i and z0 = 0. Then:

z1 = c = 1+2i

z2 = (1+2i)² + 1+2i =

z2 = 1 + 2*1*2i + 4i² + 1+2i =

z2 = 1 + 4i - 4 + 1+2i = -2 + 6i

z3 = (-2 + 6i)² + 1+2i =

z3 = 4 + 2*(-2)*6i + 36i² + 1+2i =

z3 = 4 - 24i - 36 + 1+2i = -31 -22i