Because for complex numbers abs(number) will return magnitude of Complex Numbers.

Magnitude value will counted as : √x2+y2 = √(3² + 4²) = √(9 + 16) = √(25) = 5.0

So abs with complex number will return magnitude of complex numbers.

for further reference you can use https://www.geeksforgeeks.org/abs-in-python/.

In the formula, the numerator is the dot product of two vectors, and the denominator is the product of the norms of the two vectors.

Here is a simple way to write your formula:

import math

def dot_product(u, v):
  (x1, y1) = u
  (x2, y2) = v
  return x1 * x2 + y1 * y2

def norm(u):
  (x, y) = u
  return math.sqrt(x * x + y * y)

def get_angle(u, v):
  return math.acos( dot_product(u,v) / (norm(u) * norm(v)) )

def make_vector(p, q):
  (x1, y1) = p
  (x2, y2) = q
  return (x2 - x1, y2 - y1)

#first direction vector

#punt 1, PQ
#   [x,y]
P = (1,1)
Q = (5,3)

#punt 2, RS
R = (2,3)
S = (4,1)

angle = get_angle(make_vector(p,q), make_vector(r,s))

print(angle)

abs(...)
    abs(a) -- Same as abs(a).

No, I don’t think there’s some other fancy way you don’t know about, or really any reason at all for this to be here at all except for consistency (since operator has methods for the other __operator__s).

You can do it with the built-in abs() function:

absolute_val = abs(x)

Otherwise, without the built-in function, use math:

absolute_val = (x ** 2) ** 0.5

What does 5 have to do with absolute value?

Following your logic:

def my_abs(value):
    """Returns absolute value without using abs function"""
    if value <= 0:
        return value * -1
    return value * 1

print(my_abs(-3.5))
>> 3.5
print(my_abs(3.5))
>> 3.5

Other, shorter solutions also exist and can be seen in the other answers.