def conj(u):
    return (u[0], -u[1])
z1 = (3, -2)
z2 = (1, -4)

print(conj(z1))
def add(u, v):
    return (u[0] + v[0], u[1] + v[1])

print(add(z1, z2))

def mul(u, v):
    return (u[0] * v[0] - u[1] * v[1], u[0] * v[1] + u[1] * v[0])

print(mul(z1, z2))

from fractions import Fraction

a = Fraction(3, 4)
b = Fraction(2, 7)
c = a + b
print(c.numerator, c.denominator)
print(c)

z1 = (Fraction(1, 2), Fraction(-3, 2))
z2 = (Fraction(-2, 3), Fraction(1, 4))
print(mul(z1, z2))

def div(u, v):
    return (Fraction(u[0] * v[0] + u[1] * v[1], v[0]**2 + v[1]**2),
            Fraction(-u[0] * v[1] + u[1] * v[0], v[0]**2 + v[1]**2))
print(div(z1, z2))

def div1(u, v):
    x, y = mul(u, conj(v))
    den = mul(v, conj(v))
    return (Fraction(x, den[0]), Fraction(y, den[0]))

print(div1(z1, z2))