Complex Module#

Complex Class#

Contains the class Complex, which implements the notion of complex number

class complex.complex.Complex(real: Optional[Union[float, Complex]] = None, imaginary: Optional[float] = None, norm: Optional[float] = None, theta: Optional[float] = None, from_string: Optional[str] = None, from_complex: Optional[Complex] = None)#

Complex Number

Variables:

real (float) –
imaginary (float) –
norm (float) –
theta (float) –

__add__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> znumber2 = Complex(5, 6)
>>> print(znumber + znumber2)
8.0 + 10.0i
>>> znumber2 = "5 + 6i"
>>> print(znumber + znumber2)
8.0 + 10.0i
>>> znumber2 = 5
>>> print(znumber + znumber2)
8.0 + 4.0i

__eq__(other: Union[int, float, Complex, str]) → bool#

Example

>>> znumber = Complex(3, 4)
>>> znumber2 = Complex(norm=5, theta=0.9272952180016123)
>>> znumber == znumber2
True

__iadd__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> znumber += Complex(5, 6)
>>> print(znumber)
8.0 + 10.0i

__idiv__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(norm=3, theta=4)
>>> znumber /= Complex(norm=5, theta=6)
>>> print(znumber.to_string("exp"))
0.6e^-2.0i

__imul__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(norm=3, theta=4)
>>> znumber *= Complex(norm=5, theta=6)
>>> print(znumber.to_string("exp"))
15.0e^10.0i

__init__(real: Optional[Union[float, Complex]] = None, imaginary: Optional[float] = None, norm: Optional[float] = None, theta: Optional[float] = None, from_string: Optional[str] = None, from_complex: Optional[Complex] = None)#

You can initialise the Complex class in one of the following ways:

By giving another complex number as first argument or a from_complex argument

By giving real and imaginary part as first two arguments

By giving explicitely norm= and theta=

By giving a mathematical expression as the from_string argument

See example below. No matter the method you choose, the real and imaginary parts along with norm and argument are set. If you modify any of those, the other 3 will be modified accordingly.

Parameters:

real (Optional[Union[float, "Complex"]]) –
imaginary (Optional[float]) –
norm (Optional[float]) –
theta (Optional[float]) –
from_string (Optional[str]) – String representation
from_complex (Optional[Complex]) – Another complex number to copy

Examples

>>> znumber = Complex(3, 4)
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
5.0
>>> print(znumber.theta)
0.9272952180016123

>>> znumber = Complex(3, 4, 5, 0.9)
Traceback (most recent call last):
  ...
ValueError: You specified both cartesian and trigo representations but the values are not compatible
>>> znumber = Complex(3, 4, 5, 0.9272952180016123)

>>> znumber = Complex(norm=5, theta=0.9272952180016123)
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
5.0
>>> print(znumber.theta)
0.9272952180016123

>>> znumber = Complex(from_string="3+4i")
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
5.0
>>> print(znumber.theta)
0.9272952180016123

>>> znumber = Complex(from_string="3")
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
0.0
>>> print(znumber.norm)
3.0
>>> print(znumber.theta)
0.0

>>> znumber = Complex(from_string="4i")
>>> print(znumber.real)
0.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
4.0
>>> print(znumber.theta)
1.5707963267948966

>>> znumber = Complex(from_string="3cos(0)")
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
0.0
>>> print(znumber.norm)
3.0
>>> print(znumber.theta)
0.0

>>> znumber = Complex(from_string="4isin(1.5707963267948966)")
>>> print(znumber.real)
0.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
4.0
>>> print(znumber.theta)
1.5707963267948966

>>> # In case your string can not be a complex (here we would have two different r for instance),
>>> # it is the part in 'cos' that is used.
>>> znumber = Complex(from_string="3cos(4) + 4isin(1)")
>>> print(znumber.real)
-1.960930862590836
>>> print(znumber.imaginary)
-2.2704074859237844
>>> print(znumber.norm)
3.0
>>> print(znumber.theta)
4.0

>>> znumber = Complex(from_string="3 + 4 * i")
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
5.0
>>> print(znumber.theta)
0.9272952180016123

>>> znumber = Complex(from_string="5e^0.9272952180016123i")
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
5.0
>>> print(znumber.theta)
0.9272952180016123

>>> znumber = Complex(from_string="5*(cos(0.9272952180016123i) + isin(0.9272952180016123i)")
>>> print(znumber.real)
3.0
>>> print(znumber.imaginary)
4.0
>>> print(znumber.norm)
5.0
>>> print(znumber.theta)
0.9272952180016123

>>> znumber_2 = Complex(from_complex=znumber)
>>> print(znumber_2.real)
3.0
>>> print(znumber_2.imaginary)
4.0
>>> print(znumber_2.norm)
5.0
>>> print(znumber_2.theta)
0.9272952180016123

>>> znumber_2 = Complex(znumber)
>>> print(znumber_2.real)
3.0
>>> print(znumber_2.imaginary)
4.0
>>> print(znumber_2.norm)
5.0
>>> print(znumber_2.theta)
0.9272952180016123

__ipow__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(norm=3, theta=4)
>>> znumber **= Complex(norm=5, theta=6)
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for ** or pow(): 'Complex' and 'Complex'
>>> znumber **= "5e^6i"
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for ** or pow(): 'Complex' and 'str'
>>> znumber **= 5
>>> print(znumber.to_string("exp"))
243.0e^20.0i

__isub__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> znumber -= Complex(5, 6)
>>> print(znumber)
-2.0 - 2.0i

__mul__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(norm=3, theta=4)
>>> znumber2 = Complex(norm=5, theta=6)
>>> print((znumber * znumber2).to_string("exp"))
15.0e^10.0i
>>> znumber2 = "5e^6i"
>>> print((znumber * znumber2).to_string("exp"))
15.0e^10.0i
>>> znumber2 = 5
>>> print((znumber * znumber2).to_string("exp"))
15.0e^4.0i

__ne__(other: Union[int, float, Complex, str]) → bool#

Example

>>> znumber = Complex(3, 4)
>>> znumber2 = Complex(norm=5, theta=0.9272952180016123)
>>> znumber != znumber2
False

__neg__() → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> z2 = -znumber
>>> print(z2)
-3.0 - 4.0i

__pow__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(norm=3, theta=4)
>>> znumber2 = Complex(norm=5, theta=6)
>>> print((znumber ** znumber2).to_string("exp"))
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for ** or pow(): 'Complex' and 'Complex'
>>> znumber2 = "5e^6i"
>>> print((znumber ** znumber2).to_string("exp"))
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for ** or pow(): 'Complex' and 'str'
>>> znumber2 = 5
>>> print((znumber ** znumber2).to_string("exp"))
243.0e^20.0i

__radd__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> print(1 + znumber)
4.0 + 4.0i

__rmul__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> print(2 * znumber)
6.0 + 8.0i

__rsub__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> print(1 - znumber)
2.0 + 4.0i

__rtruediv__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> print(3 / znumber)
0.36 - 0.48i

__setattr__(key, value)#

Examples

>>> z = Complex(3, 4)
>>> z.norm
5.0
>>> z.q = 2
Traceback (most recent call last):
...
complex.ForbiddenAssignmentError: The Complex class does not allow for new attributes assignment
>>> z.real = 4
>>> z.norm
5.656854249492381
>>> z.__norm = 4
Traceback (most recent call last):
...
complex.ForbiddenAssignmentError: The Complex class does not allow for new attributes assignment

__sub__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(3, 4)
>>> znumber2 = Complex(5, 6)
>>> print(znumber - znumber2)
-2.0 - 2.0i
>>> znumber2 = "5 + 6i"
>>> print(znumber - znumber2)
-2.0 - 2.0i
>>> znumber2 = 5
>>> print(znumber - znumber2)
-2.0 + 4.0i

__truediv__(other: Union[int, float, Complex, str]) → Complex#

Examples

>>> znumber = Complex(norm=3, theta=4)
>>> znumber2 = Complex(norm=5, theta=6)
>>> print((znumber / znumber2).to_string("exp"))
0.6e^-2.0i
>>> znumber2 = "5e^6i"
>>> print((znumber / znumber2).to_string("exp"))
0.6e^-2.0i
>>> znumber2 = 5
>>> print((znumber / znumber2).to_string("exp"))
0.6e^4.0i

property cartesian#: Is true if the complex number was created from real and imaginary parts, and not from norm and thera

ceil() → Complex#

Use math.ceil method to create a new complex number

Return type:: Complex

Examples

>>> znumber = Complex(3.123456, 4.789101112)
>>> print(znumber.ceil())
4.0 + 5.0i
>>> print((znumber.ceil(repres="exp")).to_string("exp"))
6.0e^1.0i

property conjugate: Complex#

Returns the complex conjugate of this complex number

Return type:: Complex

floor() → Complex#

Use math.floor method to create a new complex number

Return type:: Complex

Examples

>>> znumber = Complex(3.123456, 4.789101112)
>>> print(znumber.floor())
3.0 + 4.0i
>>> print((znumber.floor(repres="exp")).to_string("exp"))
5.0e^0.0i

property imaginary: float#

Imaginary part.

If modified, recomputes norm and argument by using complex.Complex.r_theta_from_ab

property norm: float#

Norm.

If modified, recomputes real and imaginary parts by using complex.Complex.ab_from_r_theta

plot(fig: Optional[Figure] = None, **kwargs) → Figure#

Plots the complex number and returns a plotly.graph_objs.Figure object

Parameters:

fig (Optional[Figure]) – Figure to plot in. Will create one if not specified
kwargs – Any keyword argument to pass to plotly.express.scatter (if fig is None) or plotly.graph_objects.Scatter (if fig is not None)

Return type:

Figure

property real: float#

Real part.

If modified, recomputes norm and argument by using complex.Complex.r_theta_from_ab

round(rount_to: int) → Complex#

Returns another complex number with rounded attributes using builting round method.

Parameters:: rount_to (int) –
Return type:: Complex

Examples

>>> znumber = Complex(3.123456, 4.789101112)
>>> print(znumber.round(rount_to=2))
3.12 + 4.79i
>>> print((znumber.round(rount_to=2, repres="exp")).to_string("exp"))
5.72e^0.99i

property theta: float#

Argument.

If modified, recomputes real and imaginary parts by using complex.Complex.ab_from_r_theta

to_latex(repres: str = 'cartesian') → str#

Formats the complex number into a LaTeX expression

Parameters:: repres (str) – Can be “cartesion”, “exp” or “trigo”
Return type:: str

Examples

>>> z = Complex(3, 3)
>>> print(z.to_latex())
$3.0 + 3.0i$
>>> print(z.to_latex("trigo"))
$4.242640687119285 \times (\cos(0.7853981633974483) + i \sin(0.7853981633974483))$
>>> print(z.to_latex("exp"))
$4.242640687119285 \text{e}^{0.7853981633974483 i}$

Raises:: ValueError – If given ‘repres’ argument is not “cartesian”, “trigo” nor “exp”

to_repr(repres: str = 'cartesian') → str#

str readable by exec() or eval()

Parameters:: repres (str) – Can be “cartesion”, “exp” or “trigo”
Return type:: str

Examples

>>> z = Complex(3, 3)
>>> print(repr(z))
3.0 + 3.0 * i
>>> print(z.to_repr("trigo"))
4.242640687119285 * (cos(0.7853981633974483) + i * sin(0.7853981633974483))
>>> print(z.to_repr("exp"))
4.242640687119285 * e ** (0.7853981633974483 * i)

Raises:: ValueError – If given ‘repres’ argument is not “cartesian”, “trigo” nor “exp”

to_string(repres: str = 'cartesian') → str#

Human-readable str

Parameters:: repres (str) – Can be “cartesion”, “exp” or “trigo”
Return type:: str

Examples

>>> z = Complex(3, 3)
>>> print(z)
3.0 + 3.0i
>>> print(z.to_string("trigo"))
4.242640687119285 * (cos(0.7853981633974483) + isin(0.7853981633974483))
>>> print(z.to_string("exp"))
4.242640687119285e^0.7853981633974483i

Raises:: ValueError – If given ‘repres’ argument is not “cartesian”, “trigo” nor “exp”

trunc() → Complex#

Use math.trunc method to create a new complex number

Return type:: Complex

Examples

>>> znumber = Complex(3.123456, 4.789101112)
>>> print(znumber.trunc())
3.0 + 4.0i
>>> print((znumber.trunc(repres="exp")).to_string("exp"))
5.0e^0.0i

exception complex.complex.ForbiddenAssignmentError#: Home-made class used to tell the user that Complex does not allow for new attributes assignment. I.e, one can do ‘some_complex_number.a = 0’, but not ‘some_complex_number.foo = 0’, for ‘foo’ is not a known attribute of the class.

Functions#

Some arithmetic and trigonometric-related functions

complex.functions.ab_from_r_theta(norm: float, theta: float) → Tuple[float, float]#

Returns real and imaginary part of real complex number from its norm and argument

Parameters:

norm (float) –
theta (float) –

Returns:

real and imaginary parts

Return type:

Tuple[float, float]

complex.functions.compatible_numbers(n_1: float, n_2: float, threshold: float = 1e-08) → bool#: Returns True if both numbers are equal or almost the same

complex.functions.r_theta_from_ab(real: float, imaginary: float) → Tuple[float, float]#

Returns norm and argument of a complex number from the real and imaginary parts

Parameters:

real (float) –
imaginary (float) –

Returns:

Norm and argument

Return type:

Tuple[float, float]