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

14x

Step-by-step explanation:

multiply the 2i by the 0 eulogistic quotient

z1 = 1+2i

z2 = - 2 + 6i

z3 = - 31 - 22i

Step-by-step 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