class Complex:
    def __init__(self, real=0.0, imag=0.0):
        self.real = real
        self.imag = imag

    def __add__(self, other):
        if isinstance(other, Complex):
            return Complex(self.real + other.real, self.imag + other.imag)
        return NotImplemented

    def __sub__(self, other):
        if isinstance(other, Complex):
            return Complex(self.real - other.real, self.imag - other.imag)
        return NotImplemented

    def __mul__(self, other):
        if isinstance(other, Complex):
            return Complex(
                self.real * other.real - self.imag * other.imag,
                self.real * other.imag + self.imag * other.real
            )
        return NotImplemented

    def __truediv__(self, other):
        if isinstance(other, Complex):
            denom = other.real ** 2 + other.imag ** 2
            if denom == 0:
                raise ZeroDivisionError("division by zero")
            return Complex(
                (self.real * other.real + self.imag * other.imag) / denom,
                (self.imag * other.real - self.real * other.imag) / denom
            )
        return NotImplemented

    def __str__(self):
        return f"{self.real} + {self.imag}i"

    def __repr__(self):
        return f"Complex({self.real}, {self.imag})"

    def conjugate(self):    
        return Complex(self.real, -self.imag)

    def magnitude(self):
        return (self.real ** 2 + self.imag ** 2) ** 0.5

    def phase(self):
        import math
        return math.atan2(self.imag, self.real)

    def __eq__(self, other):
        if isinstance(other, Complex):
            return self.real == other.real and self.imag == other.imag
        return NotImplemented

    def __ne__(self, other):
        return not self.__eq__(other)       

if __name__ == "__main__":
    c1 = Complex(3, 4)
    c2 = Complex(1, 2)
    
    print("c1:", c1)
    print("c2:", c2)
    print("c1 + c2:", c1 + c2)
    print("c1 - c2:", c1 - c2)
    print("c1 * c2:", c1 * c2)
    print("c1 / c2:", c1 / c2)
    print("Conjugate of c1:", c1.conjugate())
    print("Magnitude of c1:", c1.magnitude())
    print("Phase of c1:", c1.phase())
    print("Are c1 and c2 equal?", c1 == c2)