Solved Unit 1 Assignment: Creating a Puzzle Follow the | Chegg.com - Free Printable

Since you've uploaded an image with instructions for a Unit 1 Assignment: Creating a Puzzle, but no actual image of the puzzle itself is visible in your message (as this is text-based), I’ll help you create and solve a sample puzzle based on the assignment description.

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✔ Understanding the Assignment

You are to create a 3×3 puzzle grid (9 squares) where:
- Each square has 4 sides (top, right, bottom, left).
- The edges of adjacent squares must match — meaning matching mathematical expressions or values.
- There are 12 matching pairs (24 entries total), and 12 extra entries to fill the outer edges.
- You need to include 12 specific types of problems related to:
- Polar ↔ Rectangular coordinates
- Absolute value of complex numbers
- Polar ↔ Rectangular equations
- Powers of imaginary/complex numbers
- Operations with complex numbers (addition, subtraction, multiplication, division)

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## 🧩 Step-by-Step: Create & Solve a Puzzle

We will now design a complete puzzle that satisfies all requirements. Since I can't draw images, I'll provide:

1. A text representation of the puzzle layout.
2. The matching pairs with full solutions.
3. A completed version showing how they connect.
4. All required math work.

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🔢 Step 1: Define the 12 Matching Pairs

Let’s create 12 pairs (each pair matches two expressions). We’ll assign them to edges of squares so that adjacent sides match.

| Pair | Type | Expression A | Expression B |
|------|------|--------------|--------------|
| 1 | Polar ↔ Rectangular | $ (3, \frac{\pi}{6}) $ | $ \left(\frac{3\sqrt{3}}{2}, \frac{3}{2}\right) $ |
| 2 | Polar ↔ Rectangular | $ (4, \frac{3\pi}{4}) $ | $ (-2\sqrt{2}, 2\sqrt{2}) $ |
| 3 | Absolute Value | $ |3 + 4i| $ | $ 5 $ |
| 4 | Absolute Value | $ |-2 + i| $ | $ \sqrt{5} $ |
| 5 | Polar ↔ Rectangular Equation | $ r = 2\cos\theta $ | $ x^2 + y^2 = 2x $ |
| 6 | Polar ↔ Rectangular Equation | $ r = 4\sin\theta $ | $ x^2 + y^2 = 4y $ |
| 7 | Power of Complex Number | $ i^5 $ | $ i $ |
| 8 | Power of Complex Number | $ (1+i)^2 $ | $ 2i $ |
| 9 | Addition | $ (2 + 3i) + (1 - i) $ | $ 3 + 2i $ |
| 10 | Subtraction | $ (5 - 2i) - (1 + 4i) $ | $ 4 - 6i $ |
| 11 | Multiplication | $ (2 + i)(1 - i) $ | $ 3 - i $ |
| 12 | Division | $ \frac{3 + 3i}{1 - i} $ | $ 3i $ |

> ✔ These 12 pairs cover all required categories:
> - 2 polar ↔ rectangular coordinates → Pairs 1, 2
> - 2 absolute value → Pairs 3, 4
> - 2 polar ↔ rectangular equations → Pairs 5, 6
> - 2 powers → Pairs 7, 8
> - 4 operations → Pairs 9–12 (add, sub, mult, div)

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🧱 Step 2: Design the 3×3 Grid Layout

Each square has 4 edges: top, right, bottom, left.

We'll label squares as:

```
[ A ] [ B ] [ C ]
[ D ] [ E ] [ F ]
[ G ] [ H ] [ I ]
```

We’ll assign matching pairs to adjacent edges so that:
- Right edge of A = Left edge of B
- Bottom edge of A = Top edge of D
- etc.

We’ll place the 12 matching pairs across internal edges (12 shared edges in a 3×3 grid).

There are:
- 3 horizontal internal lines → 3 × 3 = 9 shared edges? No — actually:
- Horizontal shared edges: between rows → 2 rows × 3 columns = 6
- Vertical shared edges: between columns → 3 rows × 2 columns = 6
- Total = 12 shared edges → perfect!

So we have 12 internal edges → perfect for 12 matching pairs.

We’ll assign each pair to one edge.

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🎯 Step 3: Assign Matching Pairs to Edges

Let’s assign:

#### 🔹 Horizontal Shared Edges (between rows):
- Between A-B-C and D-E-F:
- A-bottom = D-top → Pair 1: $ (3, \frac{\pi}{6}) $ ↔ $ \left(\frac{3\sqrt{3}}{2}, \frac{3}{2}\right) $
- B-bottom = E-top → Pair 2: $ (4, \frac{3\pi}{4}) $ ↔ $ (-2\sqrt{2}, 2\sqrt{2}) $
- C-bottom = F-top → Pair 3: $ |3+4i| $ ↔ $ 5 $

- Between D-E-F and G-H-I:
- D-bottom = G-top → Pair 4: $ |-2+i| $ ↔ $ \sqrt{5} $
- E-bottom = H-top → Pair 5: $ r=2\cos\theta $ ↔ $ x^2+y^2=2x $
- F-bottom = I-top → Pair 6: $ r=4\sin\theta $ ↔ $ x^2+y^2=4y $

#### 🔹 Vertical Shared Edges (between columns):
- Between A-D-G and B-E-H and C-F-I:
- A-right = B-left → Pair 7: $ i^5 $ ↔ $ i $
- D-right = E-left → Pair 8: $ (1+i)^2 $ ↔ $ 2i $
- G-right = H-left → Pair 9: $ (2+3i)+(1-i) $ ↔ $ 3+2i $

- B-right = C-left → Pair 10: $ (5-2i)-(1+4i) $ ↔ $ 4-6i $
- E-right = F-left → Pair 11: $ (2+i)(1-i) $ ↔ $ 3-i $
- H-right = I-left → Pair 12: $ \frac{3+3i}{1-i} $ ↔ $ 3i $

Now, we assign one expression from each pair to each edge.

Let’s build the grid.

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🧩 Step 4: Fill the Grid (Original Puzzle)

We’ll write the expression on each side of each square.

We’ll use A, B, C... for squares.

We'll denote:
- T = top
- R = right
- B = bottom
- L = left

We’ll assign expressions so that shared edges match.

Let’s go step by step.

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#### Square A (Top-left)
- T: Extra (e.g., $ z = 1+i $)
- R: $ i^5 $ ← matches B-left
- B: $ (3, \frac{\pi}{6}) $ ← matches D-top
- L: Extra (e.g., $ \theta = \frac{\pi}{3} $)

#### Square B (Top-center)
- T: Extra (e.g., $ r = 1 $)
- R: $ (5-2i)-(1+4i) $ ← matches C-left
- B: $ (4, \frac{3\pi}{4}) $ ← matches E-top
- L: $ i $ ← matches A-right

#### Square C (Top-right)
- T: Extra (e.g., $ x = 2 $)
- R: Extra (e.g., $ z = 2 $)
- B: $ |3+4i| $ ← matches F-top
- L: $ 4-6i $ ← matches B-right

#### Square D (Middle-left)
- T: $ \left(\frac{3\sqrt{3}}{2}, \frac{3}{2}\right) $ ← matches A-bottom
- R: $ (1+i)^2 $ ← matches E-left
- B: $ |-2+i| $ ← matches G-top
- L: Extra (e.g., $ \text{Re}(z) = 1 $)

#### Square E (Center)
- T: $ (-2\sqrt{2}, 2\sqrt{2}) $ ← matches B-bottom
- R: $ (2+i)(1-i) $ ← matches F-left
- B: $ r=2\cos\theta $ ← matches H-top
- L: $ 2i $ ← matches D-right

#### Square F (Middle-right)
- T: $ 5 $ ← matches C-bottom
- R: Extra (e.g., $ y = 1 $)
- B: $ r=4\sin\theta $ ← matches I-top
- L: $ 3-i $ ← matches E-right

#### Square G (Bottom-left)
- T: $ \sqrt{5} $ ← matches D-bottom
- R: $ (2+3i)+(1-i) $ ← matches H-left
- B: Extra (e.g., $ z = 0 $)
- L: Extra (e.g., $ \text{Im}(z) = 0 $)

#### Square H (Bottom-center)
- T: $ x^2 + y^2 = 2x $ ← matches E-bottom
- R: $ \frac{3+3i}{1-i} $ ← matches I-left
- B: Extra (e.g., $ z = 1 $)
- L: $ 3+2i $ ← matches G-right

#### Square I (Bottom-right)
- T: $ x^2 + y^2 = 4y $ ← matches F-bottom
- R: Extra (e.g., $ z = 3 $)
- B: Extra (e.g., $ \theta = \frac{\pi}{2} $)
- L: $ 3i $ ← matches H-right

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✔ Step 5: Verify All Matches

| Edge | Matched Pair | Correct? |
|------|---------------|--------|
| A-R / B-L | $ i^5 $ ↔ $ i $ | ✔ $ i^5 = i^{4+1} = (i^4)(i) = 1 \cdot i = i $ |
| B-R / C-L | $ (5-2i)-(1+4i) = 4-6i $ | ✔ $ (5-1)+(-2-4)i = 4-6i $ |
| D-R / E-L | $ (1+i)^2 = 1 + 2i + i^2 = 1 + 2i -1 = 2i $ | ✔ |
| E-R / F-L | $ (2+i)(1-i) = 2(1) -2i +i -i^2 = 2 -i +1 = 3 - i $ | ✔ |
| G-R / H-L | $ (2+3i)+(1-i) = 3+2i $ | ✔ |
| H-R / I-L | $ \frac{3+3i}{1-i} $ → multiply numerator and denominator by $ 1+i $:
$ \frac{(3+3i)(1+i)}{(1-i)(1+i)} = \frac{3(1+i)^2}{2} = \frac{3(1+2i-1)}{2} = \frac{3(2i)}{2} = 3i $ | ✔ |
| A-B / D-T | $ (3, \frac{\pi}{6}) $ → $ x = 3\cos(\pi/6) = 3 \cdot \frac{\sqrt{3}}{2} = \frac{3\sqrt{3}}{2} $, $ y = 3\sin(\pi/6) = 3 \cdot \frac{1}{2} = \frac{3}{2} $ | ✔ |
| B-B / E-T | $ (4, 3\pi/4) $ → $ x = 4\cos(3\pi/4) = 4(-\frac{\sqrt{2}}{2}) = -2\sqrt{2} $, $ y = 4\sin(3\pi/4) = 4(\frac{\sqrt{2}}{2}) = 2\sqrt{2} $ | ✔ |
| C-B / F-T | $ |3+4i| = \sqrt{3^2+4^2} = \sqrt{25} = 5 $ | ✔ |
| D-B / G-T | $ |-2+i| = \sqrt{(-2)^2 + 1^2} = \sqrt{5} $ | ✔ |
| E-B / H-T | $ r = 2\cos\theta $ → $ r^2 = 2r\cos\theta $ → $ x^2 + y^2 = 2x $ | ✔ |
| F-B / I-T | $ r = 4\sin\theta $ → $ r^2 = 4r\sin\theta $ → $ x^2 + y^2 = 4y $ | ✔ |

All 12 pairs match correctly.

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📐 Step 6: Submit Requirements

You should submit:

1. Picture of original puzzle → Use a grid with 9 squares, label each edge with one expression (not both).
- For example, only show $ i^5 $ on A-right, not $ i $.
- Only show $ (3,\pi/6) $ on A-bottom, not the rectangular form.
- Outer edges: fill with extras like “$ z=1 $”, “$ \theta=\pi/3 $”, etc.

2. Picture of solved puzzle → Show both expressions on matching edges (e.g., $ i^5 $ and $ i $ connected).

3. Work for each pair → We’ve already shown all above.

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✔ Final Answer Summary

You now have a fully designed puzzle that meets all criteria:

- 9 squares in 3×3 grid
- 12 matching pairs covering:
- 2 polar ↔ rect coordinates
- 2 absolute values
- 2 polar ↔ rect equations
- 2 powers
- 4 operations
- 12 extra entries for outer edges
- All math verified

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📝 How to Turn It In

1. Draw the original puzzle (9 squares, 4 edges labeled with one expression per edge, no duplicates).
2. Draw the solved puzzle (show both expressions on matching edges).
3. Write up all 12 solution steps (like we did above).
4. Include a brief explanation of how each pair fits.

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Would you like me to generate a printable version of the puzzle (in text format) or help you draw it using ASCII art?