class ComplexNumber:
    def __init__(self, real, imag):
        self.real = real
        self.imag = imag

    def __str__(self):
        if self.real == 0:
            return f'{self.imag:g}j'
        if self.imag < 0:
            return f'({self.real:g}{self.imag:g}j)'
        return f'({self.real:g}+{self.imag:g}j)'

    def __abs__(self):
        return (self.real ** 2 + self.imag ** 2) ** 0.5
    
    def __eq__(self, other):
        return self.real == other.real and self.imag == other.imag
    
    def __add__(self, other):
        return ComplexNumber(self.real + other.real, self.imag + self.imag)
    
    def __sub__(self, other):
        return ComplexNumber(self.real - other.real, self.imag - other.imag)
    
    def __mul__(self, other):
        return ComplexNumber(self.real * other.real - self.imag * other.imag, self.real * other.imag + self.imag * other.real)

    def __truediv__(self, other):
        sr, si, orr, oi = self.real, self.imag, other.real, other.imag
        r = float(orr**2 + oi**2)
        return ComplexNumber((sr*orr+si*oi) / r, (si*orr-sr*oi) / r)
    
    def conjugate(self):
        return ComplexNumber(self.real, -self.imag)
    

def test_ComplexNumber(a, b):
    py_cnum, my_cnum = complex(a, b), ComplexNumber(a, b)
    # Validate the constructor.
    if my_cnum.real != a or my_cnum.imag != b:
        print("__init__() set self.real and self.imag incorrectly")
    # Validate conjugate() by checking the new number's imag attribute.
    if py_cnum.conjugate().imag != my_cnum.conjugate().imag:
        print("conjugate() failed for", py_cnum)
    # Validate __str__().
    if str(py_cnum) != str(my_cnum):
        print("__str__() failed for", py_cnum)
    # Validate __abs__().
    if str(abs(py_cnum)) != str(abs(my_cnum)):
        print("__abs__() failed for", py_cnum)
    # Validate __eq__().
    if str(py_cnum) != str(my_cnum):
        print("__eq__() failed for", py_cnum)
    # Validate __add__().
    if str(py_cnum + py_cnum) != str(my_cnum + my_cnum):
        print(print("__add__() failed for", py_cnum))
    # Validate __sub__().
    if str(py_cnum - py_cnum) != str(my_cnum - my_cnum):
        print(print("__sub__() failed for", py_cnum))
    # Validate __mul__().
    if str(py_cnum * py_cnum) != str(my_cnum * my_cnum):
        print(print("__mul__() failed for", py_cnum))
    # Validate __truediv__().
    if str(py_cnum / py_cnum) != str(my_cnum / my_cnum):
        print(py_cnum / py_cnum, my_cnum / my_cnum)
        print(print("__truediv__() failed for", py_cnum))


test_ComplexNumber(3, 4)