# Complex numbers


from math import sqrt


def complex(re, im):
	return Complex().init(re, im)


class Complex:

	def init(self, re, im):
		self.re = float(re)
		self.im = float(im)
		return self

	def __repr__(self):
		return 'complex' + `self.re, self.im`

	def __cmp__(a, b):
		a = a.__abs__()
		b = b.__abs__()
		return (a > b) - (a < b)

	def __float__(self):
		if self.im:
			raise ValueError, 'cannot convert complex to float'
		return float(self.re)

	def __long__(self):
		return long(float(self))

	def __int__(self):
		return int(float(self))

	def __abs__(self):
		# XXX overflow?
		return sqrt(self.re*self.re + self.im*self.im)

	def __add__(a, b):
		return complex(a.re + b.re, a.im + b.im)

	def __sub__(a, b):
		return complex(a.re - b.re, a.im - b.im)

	def __mul__(a, b):
		return complex(a.re*b.re - a.im*b.im, a.re*b.im + a.im*b.re)

	def __div__(a, b):
		q = (b.re*b.re + b.im*b.im)
		re = (a.re*b.re + a.im*b.im) / q
		im = (a.im*b.re - b.im*a.re) / q
		return complex(re, im)

	def __neg__(self):
		return complex(-self.re, -self.im)


def test():
	a = complex(2, 0)
	b = complex(3, 4)
	print a, b
	print a+b, a-b, a*b, a/b
	print b+a, b-a, b*a, b/a
	i = complex(0, 1)
	print i, i*i, i*i*i, i*i*i*i
	j = complex(1, 1)
	print j, j*j, j*j*j, j*j*j*j
	print abs(j), abs(j*j), abs(j*j*j), abs(j*j*j*j)
	print i/-i

test()