#Python, 111

Longest answer so far. My motivations are 1) learn python and 2) possibly port this to pyth.

from cmath import *
q=input()
print reduce(lambda x,y:x+y,map(lambda (x,y):phase(x/y)/pi/2,zip(q[1:]+q[:1],q)))

Input is given as a list of complex numbers.

Ideone.

I think the approach is similar to the ES6 answer.

When 2 complex numbers are multiplied, the argument or phase of the product is the sum of the argument or phase of the two numbers. Thus when a complex number is divided by another, then the phase of the quotient is the difference between the phases of the numerator and denominator. Thus we can calculate the angle traversed through for each point and the next point. Sum these angles and divide by 2π gives the required winding number.

Python, 111

Longest answer so far. My motivations are 1) learn python and 2) possibly port this to pyth.

from cmath import *
q=input()
print reduce(lambda x,y:x+y,map(lambda (x,y):phase(x/y)/pi/2,zip(q[1:]+q[:1],q)))

Input is given as a list of complex numbers.

Ideone.

I think the approach is similar to the ES6 answer.

When 2 complex numbers are multiplied, the argument or phase of the product is the sum of the argument or phase of the two numbers. Thus when a complex number is divided by another, then the phase of the quotient is the difference between the phases of the numerator and denominator. Thus we can calculate the angle traversed through for each point and the next point. Sum these angles and divide by 2π gives the required winding number.

#Python, 111

Longest answer so far. My motivations are 1) learn python and 2) possibly port this to pyth.

from cmath import *
q=input()
print reduce(lambda x,y:x+y,map(lambda (x,y):phase(x/y)/pi/2,zip(q[1:]+q[:1],q)))

Input is given as a list of complex numbers.

Ideone.

I think the approach is similar to the ES6 answer.

When 2 complex numbers are multiplied, the argument or phase of the product is the sum of the argument or phase of the two numbers. Thus when a complex number is divided by another, then the phase of the quotient is the difference between the phases of the numerator and denominator. Thus we can calculate the angle traversed through for each point and the next point. Sum these angles and divide by 2π gives the required winding number.

#Python, 111

Longest answer so far. My motivations are 1) learn python and 2) possibly port this to pyth.

from cmath import *
q=input()
print reduce(lambda x,y:x+y,map(lambda (x,y):phase(x/y)/pi/2,zip(q[1:]+q[:1],q)))

Input is given as a list of complex numbers.

Ideone.

I think the approach is similar to the ES6 answer.

When 2 complex numbers are multiplied, the argument or phase of the product is the sum of the argument or phase of the two numbers. Thus when a complex number is divided by another, then the phase of the quotient is the difference between the phases of the numerator and denominator. Thus we can calculate the angle traversed through for each point and the next point. Sum these angles and divide by 2π gives the required winding number.

#Python, 111

Longest answer so far. My motivations are 1) learn python and 2) possibly port this to pyth.

from cmath import *
q=input()
print reduce(lambda x,y:x+y,map(lambda (x,y):phase(x/y)/pi/2,zip(q[1:]+q[:1],q)))

Input is given as a list of complex numbers.

Ideone.

I think the approach is similar to the ES6 answer.

When 2 complex numbers are multiplied, the argument or phase of the product is the sum of the argument or phase of the two numbers. Thus when a complex number is divided by another, then the phase of the quotient is the difference between the phases of the numerator and denominator. Thus we can calculate the angle traversed through for each point and th4e next point. Sum these angles and divide by 2π gives the required winding number.

#Python, 111

Longest answer so far. My motivations are 1) learn python and 2) possibly port this to pyth.

from cmath import *
q=input()
print reduce(lambda x,y:x+y,map(lambda (x,y):phase(x/y)/pi/2,zip(q[1:]+q[:1],q)))

Input is given as a list of complex numbers.

Ideone.

I think the approach is similar to the ES6 answer.

When 2 complex numbers are multiplied, the argument or phase of the product is the sum of the argument or phase of the two numbers. Thus when a complex number is divided by another, then the phase of the quotient is the difference between the phases of the numerator and denominator. Thus we can calculate the angle traversed through for each point and the next point. Sum these angles and divide by 2π gives the required winding number.