`1` ```exercism fetch ecmascript 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:

• 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.

## Setup

Go through the setup instructions for ECMAScript to install the necessary dependencies:

http://exercism.io/languages/ecmascript

## Requirements

Install assignment dependencies:

 `1` ```\$ npm install ```

## Making the test suite pass

Execute the tests with:

 `1` ```\$ 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 changing `xtest` to `test`.

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.