Complex Numbers in Python
Implement complex numbers.
1  exercism fetch python complexnumbers

Complex Numbers
A complex number is a number in the form a + b * i
where a
and b
are real and i
satisfies i^2 = 1
.
a
is called the real part and b
is called the imaginary part of z
.
The conjugate of the number a + b * i
is the number a  b * i
.
The absolute value of a complex number z = a + b * i
is a real number z = sqrt(a^2 + b^2)
. The square of the absolute value z^2
is the result of multiplication of z
by its complex conjugate.
The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
(a + i * b) + (c + i * d) = (a + c) + (b + d) * i
,
(a + i * b)  (c + i * d) = (a  c) + (b  d) * i
.
Multiplication result is by definition
(a + i * b) * (c + i * d) = (a * c  b * d) + (b * c + a * d) * i
.
The reciprocal of a nonzero complex number is
1 / (a + i * b) = a/(a^2 + b^2)  b/(a^2 + b^2) * i
.
Dividing a complex number a + i * b
by another c + i * d
gives:
(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c  a * d)/(c^2 + d^2) * i
.
Exponent of a complex number can be expressed as
exp(a + i * b) = exp(a) * exp(i * b)
,
and the last term is given by Euler's formula exp(i * b) = cos(b) + i * sin(b)
.
Implement the following operations:
 addition, subtraction, multiplication and division of two complex numbers,
 conjugate, absolute value, exponent of a given complex number.
Assume the programming language you are using does not have an implementation of complex numbers.
Hints
See Emulating numeric types for help on operator overloading.
Exception messages
Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.
To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
raise Exception
, you should write:
1 
raise Exception("Meaningful message indicating the source of the error")

Running the tests
To run the tests, run the appropriate command below (why they are different):
 Python 2.7:
py.test complex_numbers_test.py
 Python 3.3+:
pytest complex_numbers_test.py
Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
python m pytest complex_numbers_test.py
Common pytest
options

v
: enable verbose output 
x
: stop running tests on first failure 
ff
: run failures from previous test before running other test cases
For other options, see python m pytest h
Submitting Exercises
Note that, when trying to submit an exercise, make sure the solution is in the $EXERCISM_WORKSPACE/python/complexnumbers
directory.
You can find your Exercism workspace by running exercism debug
and looking for the line that starts with Workspace
.
For more detailed information about running tests, code style and linting, please see the help page.
Source
Wikipedia https://en.wikipedia.org/wiki/Complex_number
Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.