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
2 answers:
Answer:
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
Answer:
14x
Step-by-step explanation:
multiply the 2i by the 0 eulogistic quotient
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