complexNumbers 0.0.1

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complexNumbers

Use complex numbers in python.

1 Initial Complex

z = Complex(value)

value can be 5 different datatypes:

• int
• float
• complex
• str
• Complex

1.1 int, float

They are used when a real number should be become a complex number. (no imaginary part)

1.2 complex

Standard complex numbers also can be initialed. (e.g.: 1+1j)

1.3 str

With a string there can be entered complex numbers in the cartesian and polar form.

1.3.1 cartesian form

should be entered like this: "x+yj"

1.3.2 polar form

Modulus and argument are separated by e^. (e.g.: 1e^1)

1.4 Complex

Value can also be the same type as the own class.

2 Variables

The class has following __self__ variables.

• real: real part of the cartesian form
• imaginary: imaginary part of the cartesian form
• modulus: modulus of the polar form
• argument: argument of the polar form in the range [0; 2Pi[

3 Methods

The class can be used with the following methods:

• __add__ , __radd__ , __iadd__ equals + , +=
• __sub__ , __rsub__ , __isub__ equals - , -=
• __mul__ , __rmul__ , __imul__ equals * , *=
• __truediv__ , __rtruediv__ , __itruediv__ equals / , /=
• __pow__ equals ** ATTENTION: only real numbers can be used as power and when used to get a root only one solution returns.
• __eq__ equals ==
• __ne__ equals !=
• __abs__ equals abs() returns the modulus
• __str__ equals str() returns the number in cartesian form (e.g.: "1+1j")
• root(n) returns a list with all possible roots of the complex number. n is the power of the root (e.g.: n = 2 ... square root)

4 Example

>>> a = Complex("1+1j")
>>> b = Complex("1e^1")
>>> print(a.modulus)
1.4142135623730951
>>> print(a.argument)
0.7853981633974483
>>> print(b.real)
0.5403023058681398
>>> print(b.imaginary)
0.8414709848078965
>>> print(a+b)
1.5403023058681398+1.8414709848078965j
>>> print(a-b)
0.45969769413186023+0.1585290151921035j
>>> print(a*b)
-0.30116867893975674+1.3817732906760363j
>>> print(a/b)
1.3817732906760363-0.30116867893975674j
>>> print(a**2)
1.2246467991473535e-16+2.0000000000000004j
>>> print(b**0.5)
0.8775825618903728+0.479425538604203j
>>> print(b.root())
[0.8775825618903728+0.479425538604203j, -0.8775825618903728-0.4794255386042029j]
>>> print(abs(b)
1.0
>>> print(a == a)
True
>>> print(a != b)
True