def __mul__(self, other):
if isinstance(other, numbers.Real):
return type(self)(self.real * other, self.imag * other)
if isinstance(other, numbers.Complex):
return type(self)(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, numbers.Real):
return type(self)(self.real / other, self.imag / other)
if isinstance(other, numbers.Complex):
denom = other.real**2 + other.imag**2
return type(self)(
(self.real * other.real + self.imag * other.imag) / denom,
(self.imag * other.real - self.real * other.imag) / denom)
return NotImplemented
def __rpow__(self, other):
if isinstance(other, numbers.Complex):
a = ((other**2)
**(self.real / 2)) * math.e**(-self.imag * cmath.phase(other))
b = 0.5 * self.imag * math.log(other**
2) + self.real * cmath.phase(other)
return type(self)(1, 0) * (a * cmath.cos(b)) + type(self)(
0, 1) * (a * cmath.sin(b))
return NotImplemented
def __pow__(self, other):
i = type(self)(0, 1)
one = type(self)(1, 0)
if isinstance(other, numbers.Real):
r = abs(self)
theta = cmath.phase(self)
return (r**other) * (one * math.cos(other * theta) + i *
(math.sin(other * theta)))
elif isinstance(other, numbers.Complex):
r = abs(self)
theta = cmath.phase(self)
return (r**other) * (one * cmath.cos(other * theta) + i *
(cmath.sin(other * theta)))
return NotImplemented
def __pos__(self):
return type(self)(self)
def __neg__(self):
return type(self)(-self.real, -self.imag)
def __add__(self, other):
if isinstance(other, numbers.Complex):
return type(self)(self.real + other.real, self.imag + other.imag)
if isinstance(other, numbers.Real):
return type(self)(self.real + other, self.imag)
return NotImplemented
def __reversed__(self):
return type(self)(self.imag, self.real)
def __rmod__(self, other):
if isinstance(other, numbers.Complex):
return other + self * type(self).__ceil__(-other / self)
return NotImplemented
def __round__(self, n=None):
return type(self)(round(self.real, n), round(self.imag, n))
def __ceil__(self):
return type(self)(math.ceil(self.real), math.ceil(self.imag))
def __floor__(self):
return type(self)(math.floor(self.real), math.floor(self.imag))
def __repr__(self):
return '{type.__name__}({self.real!r}, {self.imag!r})'.format(
self=self, type=type(self))
def conjugate(self):
return type(self)(self.real, -self.imag)