Add & Subtract Complex Numbers Game

Add & Subtract Complex Numbers Game
The Add Subtract Complex Numbers Game is a mathematical training tool designed to help students master the cyclical nature of the imaginary unit i. The powers of i do not grow infinitely; instead, they rotate through a specific four-step cycle.
Scroll down the page for a more detailed explanation.
 
Check out these other Complex Numbers games:
Powers of i
Add & Subtract Complex Numbers
Multiply Complex Numbers
Divide Complex Numbers
 

 

How the “Add & Subtract Complex Numbers Game” Works

1. The “Like Terms” Strategy
   The game presents problems in the form (a + bi) ± (c + di). The core logic it reinforces is that you must handle the two parts of the complex number independently:
   Real + Real: Add or subtract the constant numbers.
   Imaginary + Imaginary: Add or subtract the coefficients of i.
   
   
2. Visualizing Vector Addition
   Under the hood, the game is teaching Vector Addition. When you add (2 + 3i) to (1 + 2i), you are essentially moving 2 units right and 3 units up, then moving another 1 unit right and 2 units up. The game helps students visualize that the final destination is 3 + 5i.
   
   
3. Key Gameplay Challenges
   The game includes specific mathematical “traps” to ensure the player truly understands the concepts:
   The Subtraction Trap: When subtracting, the game reinforces that the minus sign applies to both the real and imaginary parts of the second number.
   Example: (5 + 2i) - (1 + 4i) = (5-1) + (2-4)i = 4 - 2i.
   The “Invisible 1” Rule: If the result of the imaginary part is 1i or -1i, the game displays it as i or -i to match standard mathematical notation.
   Sign Flipping: If the imaginary part is negative, the game correctly shows a - bi instead of a + -bi.
   
   How to add & subtract complex numbers?
   The Grouping Method
   A complex number is written as a + bi. To add or subtract two of them, you simply group the like terms together.
   The Formula:
   (a + bi) + (c + di) = (a + c) + (b + d)i
   
   Step-by-Step Examples
   Addition
   Let’s add (3 + 5i) and (2 + 4i).
   Group the Real parts: 3 + 2 = 5
   Group the Imaginary parts: 5i + 4i = 9i
   Combine: 5 + 9i
   
   Subtraction (The Sign Trap)
   Subtraction is where most mistakes happen because you must distribute the negative sign to both parts of the second number.
   Let’s solve (6 + 2i) - (4 - 3i).
   Distribute the minus: 6 + 2i - 4 + 3i (Notice the -3i became +3i).
   Group the Real parts: 6 - 4 = 2
   Group the Imaginary parts: 2i + 3i = 5i
   Combine: 2 + 5i.
   
   Visualizing on the Complex Plane
   In geometry, adding complex numbers is exactly the same as adding vectors. If you plot (3 + 2i) as a point on a graph and then move according to the second number, the result is the “tip” of the combined movement.
   Horizontal movement: Represents the Real part.
   Vertical movement: Represents the Imaginary part (i).
   
   Summary Tips
   Watch the brackets: Always keep the numbers in parentheses when subtracting to avoid losing a negative sign.
   Combine at the end: Your final answer should always be in the form a + bi.
    
   

This video gives a clear, step-by-step approach to how to add and subtract complex numbers.

• Show Video

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.