// complex numbers

// load js (using node.js)

const { complex, add, multiply, sin, sqrt, pi, equal, sort, format } = require('..')

// create a complex number with a numeric real and complex part

console.log('create and manipulate complex numbers')

const a = complex(2, 3)

print(a) // 2 + 3i

// read the real and complex parts of the complex number

print(a.re) // 2

print(a.im) // 3

// clone a complex value

const clone = a.clone()

print(clone) // 2 + 3i

// adjust the complex value

a.re = 5

print(a) // 5 + 3i

// create a complex number by providing a string with real and complex parts

const b = complex('3-7i')

print(b) // 3 - 7i

console.log()

// perform operations with complex numbers

console.log('perform operations')

print(add(a, b)) // 8 - 4i

print(multiply(a, b)) // 36 - 26i

print(sin(a)) // -9.6541254768548 + 2.8416922956064i

// some operations will return a complex number depending on the arguments

print(sqrt(4)) // 2

print(sqrt(-4)) // 2i

console.log()

// create a complex number from polar coordinates

console.log('create complex numbers with polar coordinates')

const c = complex({ r: sqrt(2), phi: pi / 4 })

print(c) // 1 + i

// get polar coordinates of a complex number

const d = complex(3, 4)

console.log(d.abs(), d.arg()) // radius = 5, phi = 0.9272952180016122

console.log()

// comparision operations

// note that there is no mathematical ordering defined for complex numbers

// we can only check equality. To sort a list with complex numbers,

// the natural sorting can be used

console.log('\ncomparision and sorting operations')

console.log('equal', equal(a, b)) // returns false

const values = [a, b, c]

console.log('values:', format(values, 14)) // [5 + 3i, 3 - 7i, 1 + i]

sort(values, 'natural')

console.log('sorted:', format(values, 14)) // [1 + i, 3 - 7i, 5 + 3i]

/**

* Helper function to output a value in the console. Value will be formatted.

* @param {*} value

*/

function print (value) {

const precision = 14

console.log(format(value, precision))

}