# Google Apps Script:

**Working with complex numbers**

## How to:

Google Apps Script does not have built-in support for complex numbers, necessitating the implementation of custom functionality. Below is a basic structure for handling complex numbers, including addition, subtraction, and multiplication.

```
// Define a constructor for complex numbers
function Complex(real, imag) {
this.real = real;
this.imag = imag;
}
// Method for adding two complex numbers
Complex.prototype.add = function(other) {
return new Complex(this.real + other.real, this.imag + other.imag);
};
// Method for subtracting two complex numbers
Complex.prototype.subtract = function(other) {
return new Complex(this.real - other.real, this.imag - other.imag);
};
// Method for multiplying two complex numbers
Complex.prototype.multiply = function(other) {
return new Complex(
this.real * other.real - this.imag * other.imag,
this.real * other.imag + this.imag * other.real
);
};
// Example usage
var num1 = new Complex(3, 4);
var num2 = new Complex(1, 2);
// Add two complex numbers
var sum = num1.add(num2);
console.log(`Sum: ${sum.real} + ${sum.imag}i`); // Sum: 4 + 6i
// Subtract two complex numbers
var difference = num1.subtract(num2);
console.log(`Difference: ${difference.real} + ${difference.imag}i`); // Difference: 2 + 2i
// Multiply two complex numbers
var product = num1.multiply(num2);
console.log(`Product: ${product.real} + ${product.imag}i`); // Product: -5 + 10i
```

## Deep Dive:

The concept of complex numbers dates back to the 16th century, but it was the work of mathematicians like Euler and Gauss that solidified their place in mathematics. Despite their usefulness, complex numbers are not directly supported in JavaScript or, by extension, Google Apps Script. The lack of native support means that operations on complex numbers have to be manually implemented, as demonstrated. While this provides a good learning opportunity and sufficient functionality for basic needs, for heavy computational work requiring complex numbers, one might consider leveraging other programming environments more suited to mathematical computing, such as Python with NumPy, which offer built-in, highly optimized operations for handling complex numbers. Nevertheless, understanding and implementing basic operations in Google Apps Script is a useful exercise for those looking to broaden their programming skills and apply them in a wide range of contexts.