Newton Fractal Step

Problem

Take one Newton step of p(z) = z^2 - 2 for the complex number z given as [re, im].

The update is z_new = z - (z^2 - 2) / (2z). Implement complex arithmetic with pairs and return the result as [re, im]. Assume z is not zero.

Hint

Divide complex numbers by multiplying numerator and denominator by the conjugate.

case 1

in: [[1,0]]

expected: [1.5,0]

case 2

in: [[1,1]]

expected: [1,0]

case 3

in: [[0,1]]

expected: [0,-0.5]

case 4

in: [[2,0]]

expected: [1.5,0]

Starter codePython

def newton_fractal_step(z):
    # z is [re, im]; return [re, im]
    # Your code here
    pass

4 test cases · run your code against them in the editor