complex

Properties

>>> dir(complex)
['__abs__', '__add__', '__bool__', '__class__', '__delattr__', '__dir__', '__doc__', '__eq__', '__format__', '__ge__', '__getattribute__', '__getnewargs__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__mul__', '__ne__', '__neg__', '__new__', '__pos__', '__pow__', '__radd__', '__reduce__', '__reduce_ex__', '__repr__', '__rmul__', '__rpow__', '__rsub__', '__rtruediv__', '__setattr__', '__sizeof__', '__str__', '__sub__', '__subclasshook__', '__truediv__', 'conjugate', 'imag', 'real']

Definition

A complex number represents a value with a real part and an imaginary part, written as a + bj where a is the real component and b is the imaginary component. Complex numbers are immutable.

>>> z = 2 + 3j
>>> type(z)
<class 'complex'>

>>> complex(5)        # real only
(5+0j)

>>> complex(1, -2)    # real, imag
(1-2j)

>>> complex("3+4j")   # from string
(3+4j)

Using complex numbers

Basic arithmetic

>>> (2 + 3j) + (1 + 4j)
(3+7j)

>>> (5 + 2j) - (3 + 1j)
(2+1j)

>>> (2 + 3j) * (1 + 2j)
(-4+7j)

>>> (1 + 2j) / (1 + 1j)
(1.5+0.5j)

Magnitude, conjugate, and parts

>>> z = 3 + 4j

>>> abs(z)            # magnitude
5.0

>>> z.conjugate()     # flip the sign of the imaginary part
(3-4j)

>>> z.real, z.imag    # attributes
(3.0, 4.0)

Boolean value

Complex numbers are truthy unless both parts are zero.

>>> bool(0 + 0j)
False

>>> bool(0 + 2j)
True

Immutability

Complex numbers cannot be modified in place; operations always create new complex values.

Dunder methods

Dunder Method	Operation	Example (normal syntax)	Example (dunder call)
`__add__`	Addition	`(2+3j) + (1+4j)` → `(3+7j)`	`(2+3j).__add__(1+4j)`
`__sub__`	Subtraction	`(5+2j) - (3+1j)` → `(2+1j)`	`(5+2j).__sub__(3+1j)`
`__mul__`	Multiplication	`(2+3j)*(1+2j)` → `(-4+7j)`	`(2+3j).__mul__(1+2j)`
`__truediv__`	Division	`(1+2j)/(1+1j)` → `(1.5+0.5j)`	`(1+2j).__truediv__(1+1j)`
`__abs__`	Magnitude	`abs(3+4j)` → `5.0`	`(3+4j).__abs__()`
`__neg__`	Negation	`-(3+4j)` → `(-3-4j)`	`(3+4j).__neg__()`
`__eq__`	Equality	`(1+2j) == (1+2j)` → `True`	`(1+2j).__eq__(1+2j)`
`__bool__`	Truth value	`bool(0+0j)` → `False`	`(0+0j).__bool__()`
`__complex__`	Convert to complex	`complex(3)` → `(3+0j)`	`(3).__complex__()`
`__float__`	Convert to float	`float(3+0j)` → `3.0`	`(3+0j).__float__()`
`__repr__`	Representation	`repr(1+2j)` → `'(1+2j)'`	`(1+2j).__repr__()`
`__str__`	String conversion	`str(1+2j)` → `'(1+2j)'`	`(1+2j).__str__()`

`complex` methods and attributes

`conjugate`

Returns the complex conjugate (negates the imaginary part).

>>> (3 + 4j).conjugate()
(3-4j)

`real`

Returns the real component as a float.

>>> (5 + 2j).real
5.0

`imag`

Returns the imaginary component as a float.

>>> (5 + 2j).imag
2.0

Properties​

Definition​

Using complex numbers​

Basic arithmetic​

Magnitude, conjugate, and parts​

Boolean value​

Immutability​

Dunder methods​

complex methods and attributes​

conjugate​

real​

imag​