While recording instalment 18 of the Programming by Stealth series, I promised Allison some challenges to help listeners test and hone their understanding of the core JavaScript language. Since we’ve now covered pretty much the whole language in the series, it’s the perfect time to pause and consolidate that knowledge.

These challenges are designed to be run in the PBS JavaScript Playground. You may also find the PBS JavaScript cheatsheet helpful.

## Challenge 1 – The 12 Times Tables

Using a loop of your choice, print the 12 times tables from 12 times 1 up to and including 12 times 12.

## Challenge 2 – The Fibonacci Series

Write code to print out the Fibbonaci series of numbers, stopping after the numbers go above 1,000,000 (you may print one number that is above 1,000,000, but no more).

The first two numbers in the series are 0 and 1, after that, the next number in the series is the sum of the previous two numbers.

Build up your solution in the following way:

1. Create an array named `fibonacci` with two initial values – 0, and 1.
2. Write a `while` loop that will keep going until the value of the last element of the fibonacci array is greater than 1,000,000. Inside the `while` loop, do the following:
1. Calculate the next Fibonacci number by adding the last two elements in the `fibonacci` array together.
2. Add this new value to the end of the `fibonacci` array.
3. Print the Fibonacci series, one element per line, by converting the `fibonacci` array into a string separated by newline characters.

## Challenge 3 – FizzBuzz

This is a total cliché, and very common as an interview question. It tests if a programmer understands programming basics like loops and conditionals.

Write a program that prints the numbers from 1 to 100. But for multiples of three print “Fizz” instead of the number, and for the multiples of five print “Buzz”. For numbers which are multiples of both three and five print “FizzBuzz”.

## Challenge 4 – Factorial

Write a function to calculate the factorial of an arbitrary number. Name the function `factorial`. It’s only possible to calculate the factorial of a whole number greater than or equal to zero. If an invalid input is passed, return `NaN`.

As a reminder, the factorial of 0 is 1, and the factorial of any positive number, `n`, is defined as `n` times the factorial of `n - 1`.

You can write your solution either using a loop of your choice, or, using recursion.

Test your function by calculating the factorial of the inputs in the PBS playground. If no inputs are set, print a message telling the user to enter numbers into the inputs.

## Challenge 5 – Complex Numbers

Build a prototype to represent a complex number. In case you’re a little rusty on the details, this page offers a really nice explanation of complex numbers. The prototype should be named `ComplexNumber`.

Build up your solution in the following way:

1. Define a constructor function for your prototype (it must be named the same as the prototype we are building, i.e. `ComplexNumber`).

1. For now, the constructor will not take any arguments.
2. In the constructor, Initialise a key named `_real` to the value 0.
3. Also Initialise a key named `_imaginary` to the value 0.

2. Add a so-called accessor function to the prototype to get or set the real part of the complex number. Name the function `real`.

1. If no arguments are passed, the function should return the current value of the `_real` key.
2. If there is a first argument, make sure it’s a number. If it’s not, throw an error. If it is, set it as the value of the `_real` key, and return a reference to the current object (i.e. `this`). (This will enable a technique known as function chaining, which we’ll see in action shortly.)

3. Create a similar accessor function for the imaginary part of the complex number, and name it `imaginary`.

4. Add a function to the prototype named `toString`. This function should return a string representation of the complex number. The rendering should adhere to the following rules:

1. In the general case, where both real and imaginary parts are non-zero, return a string of the following form: `'(2 + 3i)'`. If the imaginary number is negative, change the `+` to a `-`.
2. If the imaginary part is exactly 1, just show it as `i`.
3. If either of the parts are equal to zero, omit the parentheses.
4. If the real and imaginary parts are both zero, just return the string `'0'`.
5. If only the imaginary part is zero, return just the real part as a string.
6. If only the real part is zero, return just the imaginary part as a string followed by the letter `i`.

5. Test what you have so far with the following code:

6. Add a function named `parse` to the `ComplexNumber` prototype to update the value stored in the calling complex number object. This function should allow the new value be specified in a number of different ways. The following should all work:

1. Two numbers as arguments – first the real part, then the imaginary part.
2. An array of two numbers as a single argument – the first element in the array being the real part, the second the imaginary part.
3. A string of the form `(a + bi)` or `(a - bi)` where `a` is a positive or negative number, and `b` is a positive number.
4. An object with the prototype `ComplexNumber`.

7. Test the parse function you just created with the following code:

8. Update your constructor so that it can accept the same arguments as the `.parse()` function. Do not copy and paste the code, instead, update the constructor function to check if there are one or two arguments, and if there are, call the `parse` function with the appropriate arguments.

9. Test your updated constructor with the following code:

10. Add a function named `add` to the `ComplexNumber` prototype which accepts one argument, a complex number object, and adds it to the object the function is called on. Note that you add two complex numbers by adding the real parts together, and adding the imaginary parts together.

11. In a similar vain, add function named `subtract` to the `ComplexNumber` prototype. You subtract complex numbers by subtracting the real and imaginary parts.

12. Add a function named `multiplyBy` to the `ComplexNumber` prototype. The rule for multiplying complex numbers is, appropriately enough, quite complex. It can be summed up by the following rule:

`(a+bi) x (c+di) = (ac−bd) + (ad+bc)i`

13. Add a function named `conjugateOf` to the `ComplexNumber` prototype. This function should return a new ComplexNumber object with the sign of the imaginary part flipped. I.e. `2 + 3i` becomes `2 - 3i` and vica-versa.

14. Test your arithmetic functions with the following code: