ComplexNumbersProblemSolver

Repository Containing Functions and Classes to represent complex numbers and solve common problems.
Ideally this repository should contain Python code that can be used to check solutions of simple problems with complex numbers, such as problems rising in high school or maybe first year university.

Complex class

Instantiation

This class implements a complex number. To instantiate the class you need to provide two arguments, the real part of the complex number and the imaginary part. For instance, if we have we can instantiate the class as such z = Complex(real=1, img=3) or just z = Complex(1, 3).

Main attributes

Now the complex instance z will contain common information about a complex number. Here are some examples:

• Get the real & imaginary parts

>>> print(z.real)
1
>>> print(z.img)
3

• Get the modulus and the argument

>>> print(z.modulus)
3.1622776601683795
>>> print(z.arg)
1.2490457723982544

Main functions

• Print the standard & polar representation of the complex number

>>> print(z)
1 + 3i
>>> print(z.to_polar())
'3.1622776601683795e^i1.2490457723982544'

• Can do standard operations between complex numbers

>>> z = Complex(1, 3)
>>> w = Complex(4, 1)
>>> z + w
5 + 4i
>>> z - w
-3 + 2i
>>> z * w
1 + 13i
>>> z / w
0.4117647058823529 + 0.6470588235294118i
>>> abs(z) == z.modulus  # Can use abs(z) instead of a.modulus
True

• Find conjugate and reciprocal

>>> z = Complex(1, 3)
>>> z.conjugate()
1 - 3i
>>> z.reciprocal()
0.09999999999999998 - 0.29999999999999993i

• Printing pretty angles in radians The class uses a function that tries to convert an angle into a prettier representation. For example:

>>> from math import sqrt
>>> z = Complex(sqrt(2), -sqrt(2))
>>> z.to_polar()
'2.0e^iπ/4'

Problem Solving

• We can plot a single complex number as follows:

>>> import matplotlib.pyplot as plt
>>> z = Complex(1, 3)
>>> z.plot()
... plt.plot() # Optional
<matplotlib.axes._subplots.AxesSubplot object at 0x000002309E02FCC0>

• Find polar version of a number

>>> z = Complex(sqrt(2), -sqrt(2))
>>> z.to_polar()
'2.0e^iπ/4'

• Find roots of unity (static method)

>>> Complex.find_n_unity_roots(1)
1.0
>>> Complex.find_n_unity_roots(2)
[1.0, -1.0 + 1.2246467991473532e-16i]
>>> Complex.find_n_unity_roots(3)
[1.0, -0.4999999999999998 + 0.8660254037844387i, -0.5000000000000004 - 0.8660254037844385i]

We can also pretty-print them as follows

>>> for root in Complex.find_n_unity_roots(3):
... print(root.to_polar())
1.0e^i0.0
0.9999999999999999e^i2π/3
1.0e^i-2π/3