Answer:
Option A
Explanation:
Easy-Peasy!
The function is f(x) = z^2 + c, where c=1-3i and z0 = i.
So what you have to do, is to substitute the given values of Z and C into the function:
f(x) = z^2 + c
f(x) = (i)^2 + 1 - 3i
f(x) = -1 + 1 - 3i = -3i.
Then the first value is z1 = -3i.
Then we substitute new value z1 = -3i into the fuction:
f2(x) = (-3i)^2 + 1 - 3i
f2(x) = -9 + 1 - 3i = -8 - 3i
Then the second value is: z2 = -8 - 3i
Again, we substitute the value z2 = -8 - 3i into the function:
f3(x) = (-8 - 3i)^2 + 1 -3i
f3(x) = 64 + 48i -9 + 1 - 3i = 56 + 45i
Z3 = 56+45i
So, the correct option is: Option A.