(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°.