Complex Numbers in Python
Implement complex numbers.
exercism fetch python complex-numbers
A complex number is a number in the form
a + b * i where
b are real and
i^2 = -1.
a is called the real part and
b is called the imaginary part of
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 non-zero 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.
See Emulating numeric types for help on operator overloading.
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 shold write:
raise Exception("Meaningful message indicating the source of the error")
Note that, when trying to submit an exercise, make sure the solution is in the
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exercism debug and looking for the line that starts with
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Submitting Incomplete Solutions
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