const Complex = require('@rayyamhk/complex');

const num1 = new Complex(3, 4); // 3   4i
const num2 = new Complex(-2); // -2   0i
const sum = Complex.add(num1, num2);
console.log(sum.toString()); // '1   4i'

new Complex(); // Complex.NaN
new Complex(3); // 3   0i
new Complex(Infinity); // Complex.NaN
new Complex('3'); // Complex.NaN
new Complex(3, 4); // 3   4i
new Complex(3, Infinity); // Complex.NaN

new Complex(3, 4).getReal(); // 3
new Complex(0, 1).getReal(); // 0

new Complex(3, 4).getImaginary(); // 4
Complex.ZERO.getImaginary(); // 0

new Complex(3, 4).getModulus(); // 5
Complex.ZERO.getModulus(); // 0

new Complex(3, 3).getArgument(); // π/4
Complex.ZERO.getArgument(); // undefined

new Complex(3, 4).toString(); // '3   4i'
new Complex(3.1415).toString(); // '3.1415'
Complex.NaN.toString(); // 'NaN'

Complex.isNaN(new Complex(3)); // false
Complex.isNaN(new Complex(3, 4)); // false
Complex.isNaN(new Complex(Infinity)); // true
Complex.isNaN(Complex.NaN); // true

const num1 = new Complex(3, 4);
const num2 = new Complex(3   4e-16, 4);
const num3 = new Complex(3   4e-16, 4   6e-16);
Complex.isEqual(num1, num2); // true as the diff of real parts is less than 5e-16
Complex.isEqual(num1, num3); // false as the diff of imaginary parts is greater than 5e-16

Complex.isEqual(Complex.NaN, new Complex(1 / 0)); // true as both are considered as NaN

const num1 = new Complex(3, 4);
const num2 = new Complex(-1, 2);

Complex.add(num1, num2); // 2   6i
Complex.subtract(num1, num2); // 4   2i
Complex.multiply(num1, num2); // -11   2i
Complex.divide(num1, num2); // 1 - 2i
Complex.divide(num1, Complex.ZERO); // Complex.NaN

Complex.conjugate(new Complex(3, 4)); // 3 - 4i
Complex.conjugate(new Complex(3, -4)); // 3   4i
Complex.conjugate(new Complex(-3, 4)); // -3 - 4i
Complex.conjugate(new Complex(3)); // 3 - 0i
Complex.conjugate(Complex.NaN); // Complex.NaN

Complex.inverse(new Complex(3, 4)); // 3 / 25 - 4i / 25
Complex.inverse(Complex.ZERO); // Complex.NaN

Complex.pow(z, 2); // z to the power of 2
Complex.pow(z, 1.234); // z to the power of 1.234
Complex.pow(z, 0); // Complex.ONE
Complex.pow(z, -2); // 1 divided by z to the power of 2
Complex.pow(z, 1 / 4); // one of the 4-th root of z

Complex.exp(Complex.ZERO); // Complex.ONE
Complex.exp(new Complex(3, 4)); // -13.128783... - 15.200784463...i

Complex.log(Complex.E); // Complex.ONE
Complex.log(Complex.ZERO); // Complex.NaN

Complex.sin(num); // Domain: entire complex plane C
Complex.cos(num); // Domain: entire complex plane C

Complex.tan(num); // Domain: entire complex plane C except the set { (2k 1)*π/2 : k is any integer }
Complex.tan(new Complex(Math.PI / 2)); // Complex.NaN

Complex.csc(num); // Domain: entire complex plane C except the set { kπ : k is any integer }
Complex.csc(Complex.ZERO); // Complex.NaN

Complex.sec(num); // Domain: entire complex plane C except the set { (2k 1)*π/2 : k is any integer }
Complex.sec(new Complex(Math.PI / 2)); // Complex.NaN

Complex.cot(num); // Domain: entire complex plane C except the set { kπ/2 : k is any integer }
Complex.cot(Complex.PI); // Complex.NaN

Complex.asin(num); // Domain: entire complex plane C
Complex.acos(num); // Domain: entire complex plane C
Complex.atan(num); // Domain: entire complex plane C except the set { i, -i }
Complex.acsc(num); // Domain: entire complex plane C except the set { 0 }
Complex.asec(num); // Domain: entire complex plane C except the set { 0 }
Complex.acot(num); // Domain: entire complex plane C except the set { i, -i , 0 }