Polar Form Multiplication & Division

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| By Thames
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Thames
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Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 10 | Updated: Nov 12, 2025
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1) Multiply: (r = 2, θ = 30°) m (r = 3, θ = 45°)

Explanation

Multiply moduli 2×3=6; add angles 30°+45°=75°.

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About This Quiz
Polar Form Multiplication & Division - Quiz

Multiplication and division become elegant in polar form. In this quiz, you’ll see how angles add and subtract while magnitudes multiply and divide. Try this quiz to discover how polar form simplifies operations with complex numbers.

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2) Multiply: (r = 5, θ = 120°) m (r = 2, θ = 60°)

Explanation

5×2=10; 120°+60°=180°.

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3) Divide: (r = 8, θ = 210°) ÷ (r = 2, θ = 30°)

Explanation

8 ÷ 2 = 4; 210° − 30° = 180°.

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4) Multiply: (r = 3, θ = 270°) m (r = 4, θ = 90°)

Explanation

3 × 4 = 12; 270° + 90° = 360° ≡ 0°.

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5) Divide: (r = 12, θ = 45°) ÷ (r = 3, θ = 90°)

Explanation

12 ÷ 3 = 4; 45° − 90° = −45°.

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6) Multiply: (r = 7, θ = 200°) m (r = 2, θ = 160°)

Explanation

7 × 2 = 14; 200° + 160° = 360° ≡ 0°.

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7) Divide: (r = 10, θ = 300°) ÷ (r = 2, θ = 120°)

Explanation

10 ÷ 2 = 5; 300° − 120° = 180°.

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8) Multiply: (r = 6, θ = 10°) m (r = 5, θ = 80°)

Explanation

6 × 5 = 30; 10° + 80° = 90°.

Submit
9) Divide: (r = 15, θ = 270°) ÷ (r = 3, θ = 90°)

Explanation

15 ÷ 3 = 5; 270° − 90° = 180°.

Submit
10) Multiply: (r = 2, θ = 150°) m (r = 3, θ = 210°)

Explanation

2 × 3 = 6; 150° + 210° = 360° ≡ 0°.

Submit
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Multiply: (r = 2, θ = 30°) m (r = 3, θ = 45°)
Multiply: (r = 5, θ = 120°) m (r = 2, θ = 60°)
Divide: (r = 8, θ = 210°) ÷ (r = 2, θ = 30°)
Multiply: (r = 3, θ = 270°) m (r = 4, θ = 90°)
Divide: (r = 12, θ = 45°) ÷ (r = 3, θ = 90°)
Multiply: (r = 7, θ = 200°) m (r = 2, θ = 160°)
Divide: (r = 10, θ = 300°) ÷ (r = 2, θ =...
Multiply: (r = 6, θ = 10°) m (r = 5, θ = 80°)
Divide: (r = 15, θ = 270°) ÷ (r = 3, θ = 90°)
Multiply: (r = 2, θ = 150°) m (r = 3, θ = 210°)
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