Complex Numbers in ECMAScript
Implement complex numbers.
exercism fetch ecmascript 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.
Go through the setup instructions for ECMAScript to install the necessary dependencies:
Install assignment dependencies:
$ npm install
Making the test suite pass
Execute the tests with:
$ npm test
In the test suites all tests but the first have been skipped.
Once you get a test passing, you can enable the next one by
Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.