Operations with Complex Numbers Color by Number - Free Printable

Actually, you did not upload an image — what you’ve provided is a *description* or *text-based representation* of the “Color by Number” worksheet for Algebra 2, focusing on Operations with Complex Numbers.

Since I can’t see the actual image (and there’s no file attached), I’ll explain how to solve this type of activity, based on standard “Color by Number” worksheets involving complex numbers.

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## 🎯 GOAL:
Each region in the circular design has a complex number expression (like `3i + 5i`, `-2 + 4i - 6i`, etc.). You must simplify each expression, then match the simplified result to a color key (which is usually provided in the worksheet but missing here).

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## ✏️ STEP-BY-STEP SOLUTION GUIDE:

Step 1: Understand the Math

You’re working with complex numbers: numbers of the form `a + bi`, where `a` and `b` are real numbers, and `i = √(-1)`.

Basic operations:
- Addition/Subtraction: Combine like terms (real parts with real parts, imaginary parts with imaginary parts).
- Example: `(3 + 4i) + (2 - i) = 5 + 3i`
- Multiplication: Use distributive property or FOIL, remembering that `i² = -1`.
- Example: `(2 + 3i)(1 - i) = 2(1) + 2(-i) + 3i(1) + 3i(-i) = 2 - 2i + 3i - 3i² = 2 + i + 3 = 5 + i`

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Step 2: Simplify Each Expression in the Diagram

Since I don’t have the full diagram, I’ll assume some common expressions that appear in such worksheets, based on your text snippet:

From your description, I see values like:
- `7i`
- `-14i`
- `10i`
- `32i`
- `-228i`
- `114i`
- `4i`
- `t` ← This might be a typo? Probably meant `i`?
- `11`
- `7`
- `-6i`
- `-9i`
- `-8i`
- `-216i`

Wait — some of these look like final answers already, not expressions to simplify. That suggests that perhaps the expressions were already simplified, and you just need to color based on the value.

But if we assume those are the *results*, then the coloring key would map:

| Value | Color |
|------------|-----------|
| 7i | Yellow |
| -14i | Blue |
| 10i | Pink |
| 32i | Green |
| -228i | Black |
| 114i | Magenta |
| 4i | Light Blue|
| 11 | Orange |
| 7 | Red |
| -6i | Purple |
| -9i | Teal |
| -8i | Dark Gray |

*(Note: Colors above are guessed — actual key should be in your worksheet.)*

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Step 3: Apply Coloring

Once you have the correct color assigned to each simplified value, you color the corresponding region in the circular pattern.

Example:
- If a section says `7i`, and your key says `7i → Yellow`, color that section yellow.
- If a section says `-228i`, and your key says `-228i → Black`, color it black.

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## ❗ Important Notes:

1. “t” is likely a typo — probably meant to be `i`. In complex numbers, variables like `t` aren't typically used unless specified. Check if it's `i` or if there’s context missing.

2. Some values seem extremely large (`-228i`, `114i`) — these may come from multiplying complex numbers, e.g.:
- `(12i)(-19) = -228i`
- `(6i)(19) = 114i`

3. The final picture will reveal a colorful geometric design — often symmetrical or mandala-like — once all regions are colored correctly.

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## ✔ How to Complete It Without the Image:

If you can provide:
- The actual expressions (not just the results),
- The color key (e.g., “7i = yellow”, “11 = red”, etc.),

…I can walk you through each calculation and tell you exactly which color goes where.

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## 💡 Pro Tip:

Use this trick when simplifying:
> Group real parts and imaginary parts separately.
> Remember: `i² = -1`, so if you multiply two imaginary numbers, you get a real number!

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## 🖍️ Final Answer (Summary):

Since no image was uploaded and no color key is provided, here’s what you must do:

✔ Simplify every complex expression in each region using addition, subtraction, or multiplication rules.

✔ Match each simplified result to the color key (usually listed somewhere on the worksheet).

✔ Color each region accordingly to reveal the hidden design.

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📌 If you can paste the actual expressions or describe the color key, I’ll give you the exact coloring instructions!

Otherwise, follow the steps above — you’ve got this! 😊

Let me know if you want to type out one or two expressions — I’ll solve them for you as examples!