mpclab/src/generators/math/algebra/complex-numbers/properties-and-rules/modulus.js

mpclab is a powerful problem generation module tailored for educational purposes. It enables developers and educators to create, customize, and generate a diverse range of problems across subjects like mathematics, physics, and chemistry. With flexible, d

/**
 * @file src/generators/math/algebra/complex-numbers/properties-and-rules/modulus.js
 * @description Generates problems involving the modulus (absolute value) of complex numbers. Example: |3 + 4i| = √(3² + 4²) = 5.
 */

const math = require("mathjs");
const { randomInt } = require("../../../../../utils/random");
const formatSigned = require("../../../../../utils/formatSigned");

/**
 * @function generateProblem - Generate a modulus problem for complex numbers.
 * @param {Object} options - The options for generating the problem.
 * @param {number} options.minReal - The minimum value for the real part a.
 * @param {number} options.maxReal - The maximum value for the real part a.
 * @param {number} options.minImaginary - The minimum value for the imaginary part b.
 * @param {number} options.maxImaginary - The maximum value for the imaginary part b.
 * @returns {Object} - The modulus problem.
 */
const generateProblem = (options) => {
  const a = randomInt(options.minReal, options.maxReal);
  const b = randomInt(options.minImaginary, options.maxImaginary);

  const problem = [
    {
      type: "text",
      value: `Find the modulus of ${a} ${formatSigned(`${b}i`)}.`,
    },
    { type: "formula", value: `|${a} ${formatSigned(`${b}i`)}|` },
  ];

  // Calculate modulus of the complex number
  const modulusValue = Math.sqrt(a ** 2 + b ** 2);

  // Use math.js to format modulus as a fraction
  const simplifiedFraction = math.fraction(modulusValue);
  const modulus = modulusValue.toFixed(2); // Float representation

  const steps = [
    {
      type: "text",
      value: `The modulus of a complex number is calculated as |a + bi| = √(a² + b²).`,
    },
    {
      type: "formula",
      value: `|${a} ${formatSigned(`${b}i`)}| = \\sqrt{${a}^2 ${formatSigned(
        b,
        false,
        "plus"
      )}^2}`,
    },
    {
      type: "formula",
      value: `= \\sqrt{${a ** 2} + ${b ** 2}}`,
    },
  ];

  const solution = [
    {
      type: "numeric",
      decimal: parseFloat(modulus), // Float representation
      fraction:
        simplifiedFraction.d === 1
          ? null
          : {
              s: simplifiedFraction.s,
              n: simplifiedFraction.n,
              d: simplifiedFraction.d,
            },
    },
  ];

  return {
    problem,
    steps,
    solution,
  };
};

module.exports = generateProblem;