Multiply Complex Numbers Game

Multiply Complex Numbers Game
The Multiply Complex Numbers Game is an interactive math trainer designed to help students master the FOIL method and the unique property of the imaginary unit: i² = -1.
Scroll down the page for a more detailed explanation.
 
Check out these other Complex Numbers games:
Powers of i
Plot Complex Numbers
Quadratics with Complex Roots

Add & Subtract Complex Numbers
Multiply Complex Numbers
Divide Complex Numbers

Magnitude of Complex Numbers
Distance between 2 Complex Numbers
Midpoint between 2 Complex Numbers
 

 

How to play the “Multiply Complex Numbers Game”

1. Starting the Game
   When you first open the game, you are presented with a Difficulty Menu:
   Easy Mode: Uses coefficients between 1 and 4. This is best for beginners to practice the FOIL steps without getting overwhelmed by large multiplication tables.
   Hard Mode: Uses coefficients up to 10. This challenges your ability to track negative signs and larger sums simultaneously.
   
   
2. Solving a Problem
   Once the game starts, a multiplication problem like (3 + 2i) × (1 - 4i) appears at the top. To find the correct answer, you follow these steps:
   Distribute (FOIL): Multiply the terms.
   First: 3 × 1 = 3
   Outer: 3 × -4i = -12i
   Inner: 2i × 1 = 2i
   Last: 2i × -4i = -8i²
   
   Simplify i²: Remember that i² = -1, so the “Last” term becomes: -8 × -1 = +8.
   Combine: Group the real parts (3 + 8 = 11) and the imaginary parts (-12i + 2i = -10i).
   
   
3. Making Your Choice
   You will see four possible answers in a grid.
   Select the match: Click the button you believe is correct.
   Instant Feedback: If you are right, the button turns Orange and a high-pitched chord plays. If you are wrong, the button turns Red and a low-pitched tone sounds.
   The Blank Space: Once you click, the correct answer fills in the “blue line” space to confirm the result.
   
   
4. Using the “Show Steps” 🔍 Button
   If you get a problem wrong (or even if you got it right but aren’t sure why), click the Show Steps button. A breakdown will appear showing:
   The result of each FOIL letter (F, O, I, L).
   The explicit conversion of the i² term.
   How those numbers summed up to the final result.
   
   
5. Progression
   Score Tracking: Your current score (Correct/Total) is displayed in the top right corner.
   Next Problem: After a selection is made, the “Next Problem” button appears to generate a fresh equation.
   Main Menu: You can return to the menu at any time to switch difficulties.
    
   

This video gives a clear, step-by-step approach to how to multiply complex numbers.

• Show Video

 

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

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