Distance between 2 Complex Numbers Game

Distance between 2 Complex Numbers
To find the distance between two complex numbers, you are essentially calculating the length of the line segment connecting two points on the complex plane. This is equivalent to finding the magnitude of their difference. To help you visualize the problem, the game includes an Argand Diagram, plots the points and draws the vector between them.
Scroll down the page for a more detailed explanation.
 
Check out these other Complex Numbers games:
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Plot Complex Numbers
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Add & Subtract Complex Numbers
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Magnitude of Complex Numbers
Distance between 2 Complex Numbers
Midpoint between 2 Complex Numbers
 

 

How to play the “Distance between 2 Complex Numbers” Game

1. Starting the Game
   When you first open the game, you are presented with a Difficulty Menu:
   Easy Mode (Integer Distances): In this mode, the answers will be integers.
   Hard Mode (Decimals): This mode generates random answers. You’ll need to estimate or calculate the square root to two decimal places.
   
   
2. Solving a Problem
   Find the “Difference”: Subtract the coordinates of the two numbers.
   Subtract Real parts: r₁ - r₂
   
   Subtract Imaginary parts: i₁ - i₂
   Square the Differences: Square both results from step 1.
   Apply the Theorem: Add the squares together and take the square root.
   
   The Shortcut Formula:
   \(d = \sqrt{(r_1- r_2)^2 + (i_1 - i_2)^2}\)
   
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 “?” 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:
   
   
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.
   
   
6. Pro Tips for High Scores
   Ignore the Signs: Whether the problem is 3 + 4 or -3 - 4i, the magnitude is exactly the same (5).
   Memorize Pythagorean Triples: Learning the common sets (3,4,5), (5,12,13), (8,15,17) will help you clear Easy Mode in seconds.
    
   

The Step-by-Step Process
An Example
Let’s find the distance between z₁ = 1 + 5i and z₂ = 4 + 1i.
Step 1: Subtract the real parts
(a - c) = 1 - 4 = -3
Step 2: Subtract the imaginary parts
(b - d) = 5 - 1 = 4
Step 3: Square both results
(-3)² = 9
(4)² = 16
Step 4: Add them and take the square root
\(\sqrt{9 + 16} = \sqrt{25} = 5\)
The distance between these two points is 5 units.
 

This video gives a clear, step-by-step approach to find the distance between 2 complex numbers.

• Show Video

 

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