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exercism fetch haskell complex-numbers

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 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:

Assume the programming language you are using does not have an implementation of complex numbers.

Getting Started

For installation and learning resources, refer to the exercism help page.

Running the tests

To run the test suite, execute the following command:

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stack test

If you get an error message like this...

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No .cabal file found in directory

You are probably running an old stack version and need to upgrade it.

Otherwise, if you get an error message like this...

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No compiler found, expected minor version match with...
Try running "stack setup" to install the correct GHC...

Just do as it says and it will download and install the correct compiler version:

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stack setup

Running GHCi

If you want to play with your solution in GHCi, just run the command:

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stack ghci

Feedback, Issues, Pull Requests

The exercism/haskell repository on GitHub is the home for all of the Haskell exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to help you!

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.