โจComplex
JS โฉ value โฉ object โฉ class โฉ example โฉ Complex
a class to represent complex numbers.
replit โฉ Complex
class Complex {
// โญ๏ธ static constant
static get zero() { return new Complex(0) } // 0
static get one() { return new Complex(1) } // 1
static get i() { return new Complex(0, 1) } // i
// constructor
constructor(a = 0, b = 0) {
this.x = a;
this.y = b;
}
// -z
negate() {
return new Complex(-this.x, -this.y);
}
// conjugate (x - yi)
conjugate() {
return new Complex(this.x, -this.y);
}
// z1 + z2
plus({ x, y }) {
return new Complex(x + this.x, y + this.y);
}
// z1 - z2
minus({ x, y }) {
return new Complex(this.x - x, this.y - y);
}
// z1 * z2
times({ x: c, y: d }) {
const { x: a, y: b } = this;
return new Complex(a * c - b * d, a * d + b * c);
}
// |z|^2
get magnitudeSquare() {
return this.times(this.conjugate()).x; // real number
}
// 1/z
inverse() {
// 1/z = z' / |z|^2 (where z' is conjugate of z)
return this.conjugate().times(new Complex(1/this.magnitudeSquare));
}
// z1 / z2
dividedBy(z2) {
return this.times(z2.inverse());
}
// z^n (where n is an integer)
toPower(n) {
let result = Complex.one;
if (n === 0) return result;
if (n > 0) {
while (n > 0) {
result = result.times(this);
n -= 1;
}
return result;
}
if (n < 0) {
while (n < 0) {
result = result.dividedBy(this);
n += 1;
}
return result;
}
}
// complex -> string
toString() {
const { x, y } = this;
return (
y === 0 ? `${x}` : // x
x === 0 ? `${hideOne(y)}i` : // yi
`${x} ${y < 0 ? '-' : '+'} ${hideOne(Math.abs(y))}i` // x + yi
);
function hideOne(y) {
return (
y === 1 ? `` :
y === -1 ? `-` : `${y}`
)
}
}
}
module.exports = Complex;const Complex = require('./Complex.js');
let z1 = new Complex(1, 1); // 1 + i
let z2 = new Complex(3, -4); // 3 - 4i
const i = Complex.i; // i
const one = Complex.one; // 1
z1.plus(z2), // 4 - 3i
z1.minus(z2), // -2 + 5i
z1.times(z2), // 7 - i
z1.dividedBy(z2), // -0.04 + 0.28i
i.toPower(4), // 1
z1.toPower(3), // -2 + 2i
i.inverse(), // -i
i.negate(), // -i
z1.inverse(), // 0.5 - 0.5i
z1.magnitudeSquare, // 2
[-2, -1, 0, 1, 2].map(x => z1.toPower(x).toString()),
// -0.5i, 0.5 - 0.5i, 1, 1 + i, 2iLast updated