Polar Form Multiplication & Division

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Thames
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 10 | Updated: Jan 20, 2026
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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°.

Submit

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

Explanation

10 ÷ 2 = 5; 300° − 120° = 180°.

Submit

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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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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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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