Handling Complex Numbers while returning function values

Question

I am trying to solve to the equation

f(x) = cos(x) - sqrt(x)

using Newton-Raphson Method in python

f'(x) = -sin(x) - (1/2*sqrt(x))

For my starting guess, I'm trying values form 0 to 4. It works fine from the range 0.00001 to 2.45

The graph looks like this

The problem is that beyond 2.45, It enters imaginary(complex numbers). How do I handle generating complex number with this?

import numpy as np
def eqn(x):
    return np.cos(x) - np.sqrt(x)

def eqn_derivation(x):
    return (-(1/(2*(np.sqrt(x)))) - (np.sin(x))) 

def new-raphson(eqn,eqn_derivation,start_guess,eps):
            x0=start_guess
            if funDeriv(x0) != 0:
                x1=x0-fun(x0)/funDeriv(x0)
                while np.abs(x1-x0)>eps:
                    x0=x1
                    if funDeriv(x0) != 0:
                        x1=x0-fun(x0)/funDeriv(x0)
            return x1

Wolfram Alpha suggests that 2nd iteration spits out complex numbers. I'm not sure how to return/generate/convert/handle function values returning complex numbers

Answer 1

I was able to solve the answer using the CMATH Library

import numpy as np
def eqn(x):
    return cmath.cos(x) - cmath.sqrt(x)

def eqn_derivation(x):
    return (-(1/(2*(cmath.sqrt(x)))) - (cmath.sin(x))) 

def new-raphson(eqn,eqn_derivation,start_guess,eps):
            x0=start_guess
            if funDeriv(x0) != 0:
                x1=x0-fun(x0)/funDeriv(x0)
                while np.abs(x1-x0)>eps:
                    x0=x1
                    if funDeriv(x0) != 0:
                        x1=x0-fun(x0)/funDeriv(x0)
            return x1

Output -

(0.6417, (0.6417-5.61e-28j))