Operations with Complex Numbers Clue Mystery Activity - Free Printable

It looks like you've uploaded an image of a fun, interactive algebra worksheet titled "Who Found It? Operations with Complex Numbers" from *Amusing Algebra*. This is a mystery-solving activity where students solve complex number operations to determine:

- Who found Logan Lemon’s lost homework
- Where it was found
- When it was found

The goal is to solve the clues (which are likely on a separate page not shown), then match the answers to the corresponding boxes in the grid. Once all clues are solved, only three boxes should remain unchecked, revealing the answer to the mystery.

Since I can't see the actual clues or the other page with problems, I’ll explain how this type of activity works and walk through an example based on the format.

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🔍 How the Activity Works

Each clue involves performing operations with complex numbers (addition, subtraction, multiplication, division, etc.). After solving each problem, the student finds the answer in one of the three columns:

- Who? – Names with associated complex numbers
- Where? – Locations with complex numbers
- When? – Periods/times with complex numbers

Once they find their answer, they cross off the box. At the end, only three boxes should be left unchecked — one in each column — forming the solution:
> Who found it? Where? When?

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✔ Example Walkthrough

Let's say one of the clues is:

> Simplify: $ \frac{12 - 4i}{5} $

We simplify:
$$
\frac{12 - 4i}{5} = \frac{12}{5} - \frac{4}{5}i = 2.4 - 0.8i
$$

But wait — looking at the "Where?" column, we see:
- $ \frac{12 - 4i}{5} $ → This matches exactly!

So this clue would lead to checking "Algebra Classroom" under Where?

Now suppose another clue is:

> Simplify: $ (3 + i) + (2 + 4i) $

$$
(3 + i) + (2 + 4i) = 5 + 5i
$$

But that doesn’t appear directly. However, if a clue results in $ 3 + i $, then we check Rebecca Red under Who?

Another clue might result in $ -18i $, so we check Yolanda Yellow under Who?

And if a clue gives $ -5 - 8i $, then we check Third Period under When?

After solving all clues, only three boxes remain unchecked — one in each category.

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🕵️‍♂️ Solving the Mystery

Let’s assume the final three unchecked boxes are:

- Who? → Olivia Orange ($ \frac{3i}{10} $)
- Where? → Cafeteria ($ 8i $)
- When? → Lunch ($ -10 + 76i $)

Then the answer would be:

> Olivia Orange found Logan Lemon’s homework in the Cafeteria during Lunch.

But since we don’t have the actual clues, we can’t solve it definitively.

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💡 Tips for Solving

1. Review Complex Number Operations:
- Addition/Subtraction: Combine real and imaginary parts.
- e.g., $ (a + bi) + (c + di) = (a+c) + (b+d)i $
- Multiplication: Use FOIL and remember $ i^2 = -1 $
- Division: Multiply numerator and denominator by the conjugate.

2. Look for Simplified Forms:
- For example, $ \frac{12 - 4i}{5} $ is already simplified.
- $ -18i $ is just $ 0 - 18i $
- $ -8 \pm 38i $ means two possible values: $ -8 + 38i $ and $ -8 - 38i $

3. Check All Answers Against the Grid
- Make sure your simplified answer matches exactly (or is equivalent).

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🧩 Final Note

To fully solve this puzzle, you need the clue page (not visible here). But once you solve all the complex number problems, match each answer to the corresponding box, and cross them off.

At the end, the three unchecked boxes will tell you:

> WHO? WHERE? WHEN?

If you can provide the clue problems, I can help you solve them step-by-step and reveal the mystery!

Would you like to share the clue problems now?