Consider the sequence `S(n, z) = (1 - z)(z + z**2 + z**3 + ... + z**n)` where `z` is a complex number
 and `n` a positive integer (n > 0).
When `n` goes to infinity and `z` has a correct value (ie `z` is in its domain of convergence `D`), `S(n, z)` goes to a finite limit
 `lim` depending on `z`.
Experiment with `S(n, z)` to guess the domain of convergence `D`of `S` and `lim` value when `z` is in `D`.
 Then determine the smallest integer `n` such that `abs(S(n, z) - lim) < eps`
 where `eps` is a given small real number and `abs(Z)` is the modulus or norm of the complex number Z.
 Call `f` the function `f(z, eps)` which returns `n`.
 If `z` is such that `S(n, z)` has no finite limit (when `z` is outside of `D`) `f` will return -1.
# Examples:
I is a complex number such as I * I = -1 (sometimes written `i` or `j`).
 `f(0.3 + 0.5 * I, 1e-4) returns 17`
 `f(30 + 5 * I, 1e-4) returns -1`
# Remark:
For languages that don't have complex numbers or "easy" complex numbers, a complex number `z` is represented by two real numbers `x` (real part) and `y` (imaginary part).
`f(0.3, 0.5, 1e-4) returns 17`
 `f(30, 5, 1e-4) returns -1`
# Note:
You pass the tests if `abs(actual - exoected) <= 1`
import math

def f(z, eps):
    return max(-1, math.log(eps)/math.log(math.hypot(z.real, z.imag)))
import math

def f(z, eps):
    return max(-1, math.log(eps)/math.log(math.hypot(z.real, z.imag)))