Test mpc elementary operations
------------------------------

    >>> import gmpy2 as G
    >>> from gmpy2 import mpz, mpq, mpfr, mpc
    >>> from fractions import Fraction as F
    >>> from decimal import Decimal as D
    >>> a = mpz(123)
    >>> b = mpz(456)
    >>> c = 12345678901234567890
    >>> af = mpfr("12.34")
    >>> bf = mpfr("45.67")
    >>> aq = mpq(3,11)
    >>> bq = mpq(17,2)
    >>> aj = mpc(1+2j)
    >>> bj = mpc(4+5j)

Test addition
-------------

>>> aj + bj
mpc('5.0+7.0j')
>>> bj + aj
mpc('5.0+7.0j')
>>> aj + a
mpc('124.0+2.0j')
>>> a + aj
mpc('124.0+2.0j')
>>> aj + 1
mpc('2.0+2.0j')
>>> 1 + aj
mpc('2.0+2.0j')
>>> aj + 0
mpc('1.0+2.0j')
>>> 0 + aj
mpc('1.0+2.0j')
>>> -1 + aj
mpc('0.0+2.0j')
>>> aj - 1
mpc('0.0+2.0j')
>>> aj + 1.2 == 2.2 + 2j
True

Test subtraction
----------------

>>> aj - bj
mpc('-3.0-3.0j')
>>> bj - aj
mpc('3.0+3.0j')
>>> aj - a
mpc('-122.0+2.0j')
>>> a - aj
mpc('122.0-2.0j')
>>> aj - 1
mpc('0.0+2.0j')
>>> 1 - aj
mpc('0.0-2.0j')
>>> 0 - aj
mpc('-1.0-2.0j')
>>> aj - 0
mpc('1.0+2.0j')
>>> aj - -1
mpc('2.0+2.0j')
>>> -1 - aj
mpc('-2.0-2.0j')
>>> aj - 1.2 == (1+2j) - 1.2
True

Test multiplication
-------------------

>>> aj * bj
mpc('-6.0+13.0j')
>>> bj * aj
mpc('-6.0+13.0j')
>>> aj * a
mpc('123.0+246.0j')
>>> a * aj
mpc('123.0+246.0j')
>>> aj * -1
mpc('-1.0-2.0j')
>>> aj * (0.0+1j)
mpc('-2.0+1.0j')

Test division
-------------

>>> aj / bj
mpc('0.34146341463414637+0.073170731707317069j')
>>> aj // bj
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't take floor of complex number.
>>> aj / a
mpc('0.008130081300813009+0.016260162601626018j')
>>> a / aj
mpc('24.600000000000001-49.200000000000003j')
>>> aj / 0
mpc('inf+infj')

Test modulo
-----------

>>> aj % bj
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't mod complex numbers
>>> aj % a
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't mod complex numbers
>>> a % aj
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't mod complex numbers
>>> divmod(aj, bj)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't take floor or mod of complex number.

Test operations involving NaN/Inf
---------------------------------

    >>> aj + float('inf')
    mpc('inf+2.0j')
    >>> aj + float('-inf')
    mpc('-inf+2.0j')
    >>> aj + float('nan')
    mpc('nan+2.0j')
    >>> float('inf') - aj
    mpc('inf-2.0j')
    >>> aj - float('inf')
    mpc('-inf+2.0j')
    >>> aj - float('-inf')
    mpc('inf+2.0j')
    >>> aj - float('nan')
    mpc('nan+2.0j')
    >>> aj * float('inf')
    mpc('inf+infj')
    >>> aj * float('-inf')
    mpc('-inf-infj')
    >>> aj * float('nan')
    mpc('nan+nanj')
    >>> mpc(0,0) * float('inf')
    mpc('nan+nanj')
    >>> mpc(0,0) * float('-inf')
    mpc('nan+nanj')
    >>> mpc(0,0) * float('nan')
    mpc('nan+nanj')
    >>> aj / float('inf')
    mpc('0.0+0.0j')
    >>> aj / float('-inf')
    mpc('-0.0-0.0j')
    >>> float('inf') / aj
    mpc('inf-infj')
    >>> float('-inf') / aj
    mpc('-inf+infj')

Test is_XXX
-----------

    >>> G.is_zero(mpc("0+0j"))
    True
    >>> G.is_zero(mpc("1+0j"))
    False
    >>> G.is_zero(mpc("1+1j"))
    False
    >>> G.is_zero(mpc("0+1j"))
    False
    >>> G.is_nan(mpc("nan+1j"))
    True
    >>> G.is_nan(mpc("1+nanj"))
    True
    >>> G.is_nan(mpc("nan+nanj"))
    True
    >>> G.is_nan(mpc("1+1j"))
    False
    >>> G.is_infinite(mpc("inf+1j"))
    True
    >>> G.is_infinite(mpc("-inf+1j"))
    True
    >>> G.is_infinite(mpc("1+infj"))
    True
    >>> G.is_infinite(mpc("1-infj"))
    True
    >>> G.is_infinite(mpc("inf-infj"))
    True
    >>> G.is_infinite(mpc("1+1j"))
    False
    >>> G.is_finite(mpc("0+0j"))
    True
    >>> G.is_finite(mpc("nan+0j"))
    False
    >>> G.is_finite(mpc("0+nanj"))
    False
    >>> G.is_finite(mpc("0+infj"))
    False
    >>> G.is_finite(mpc("inf+3j"))
    False