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Q9. Division (express the answers in polar form): (a) (4360 -20°)/(40-210°)

(b) (8+j 42)/(-6-j 4)

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(a) (4360 - 20°) / (40 - 210°):

1. Convert to polar form:

- 4360 = 4360∠0°

- 40 = 40∠0°

2. Divide the magnitudes:

- Magnitude result = (4360 / 40) = 109∠0°

3. Subtract the angles:

- Angle result = (0° - (-210°)) = 210°

The result in polar form for (a) is indeed 109∠210°.

(b) (8 + j42) / (-6 - j4):

1. Convert to polar form:

- For 8 + j42:

- Magnitude = √(8² + 42²) = √(64 + 1764) = √1828 ≈ 42.77

- Angle = arctan(42 / 8) ≈ 78.69°

- For -6 - j4:

- Magnitude = √((-6)² + (-4)²) = √(36 + 16) = √52 ≈ 7.21

- Angle = arctan((-4) / (-6)) ≈ 33.69°

2. Divide the magnitudes:

- Magnitude result = (42.77 / 7.21) ≈ 5.93

3. Subtract the angles:

- Angle result = (78.69° - 33.69°) ≈ 45°

So, the result in polar form for (b) is indeed approximately 5.93∠45°.

User Sunshinekitty
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