537. Complex Number Multiplication

Difficulty:
Related Topics:
Similar Questions:

    Problem

    Given two strings representing two complex numbers.

    You need to return a string representing their multiplication. Note i2 = -1 according to the definition.

    Example 1:

    Input: "1+1i", "1+1i"
    Output: "0+2i"
    Explanation: (1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i, and you need convert it to the form of 0+2i.
    

    Example 2:

    Input: "1+-1i", "1+-1i"
    Output: "0+-2i"
    Explanation: (1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i, and you need convert it to the form of 0+-2i.
    

    Note:

    Solution 1

    /**
     * @param {string} a
     * @param {string} b
     * @return {string}
     */
    var complexNumberMultiply = function(a, b) {
      var a = parse(a);
      var b = parse(b);
      var x = (a.x * b.x) - (a.y * b.y);
      var y = (a.x * b.y) + (a.y * b.x);
      return stringify(x, y);
    };
    
    var parse = function (str) {
      var res = /^(-?\d+)\+(-?\d+)i$/.exec(str);
      return { x: Number(res[1]), y: Number(res[2]) };
    };
    
    var stringify = function (x, y) {
      return `${x}+${y}i`
    };
    

    Explain:

    nope.

    Complexity:

    Solution 2

    /**
     * @param {string} a
     * @param {string} b
     * @return {string}
     */
    var complexNumberMultiply = function(a, b) {
      var a = parse(a);
      var b = parse(b);
      var x = (a.x * b.x) - (a.y * b.y);
      var y = (a.x * b.y) + (a.y * b.x);
      return stringify(x, y);
    };
    
    var parse = function (str) {
      var index = str.indexOf('+');
      var x = Number(str.substring(0, index));
      var y = Number(str.substring(index + 1, str.length - 1));
      return { x: x, y: y };
    };
    
    var stringify = function (x, y) {
      return `${x}+${y}i`
    }
    

    Explain:

    nope.

    Complexity: