z0 ≈ 0.6687∠(−0.0899) [or 0.6660 − 0.0601j] z1 ≈ 0.6687∠3.0517 [or − 0.6660 + 0.0601j] These are the answers

You seem to be presenting the results for two complex numbers in both polar and rectangular forms.

### Given:
- \( z_0 \approx 0.6687 \angle (-0.0899) \) or \( z_0 \approx 0.6660 - 0.0601j \)
- \( z_1 \approx 0.6687 \angle 3.0517 \) or \( z_1 \approx -0.6660 + 0.0601j \)

Let's break it down:

1. **Rectangular Form**: The complex number is given as \( a + bj \), where \( a \) is the real part and \( b \) is the imaginary part.
   - \( z_0 = 0.6660 - 0.0601j \)
   - \( z_1 = -0.6660 + 0.0601j \)

2. **Polar Form**: A complex number can also be written as \( r \angle \theta \), where \( r \) is the modulus (magnitude) and \( \theta \) is the argument (angle in radians).
   - \( z_0 \approx 0.6687 \angle -0.0899 \)
   - \( z_1 \approx 0.6687 \angle 3.0517 \)

#### Key Observations:
- The magnitudes \( r \) are approximately the same: \( |z_0| \approx |z_1| \approx 0.6687 \).
- The angles (arguments) are almost opposite (one is slightly negative, and the other is close to \( \pi \)).

Do you need further explanation on converting between polar and rectangular forms, or is there a specific question about these results?

Here are 5 follow-up questions to deepen understanding:
1. How do you convert a complex number from polar to rectangular form?
2. How do you find the argument of a complex number in radians?
3. What is the geometric interpretation of these two complex numbers on the complex plane?
4. How do you multiply two complex numbers in polar form?
5. How can the polar form be useful in solving AC circuit problems?

**Tip**: In polar form, the multiplication of complex numbers is simpler since you multiply their magnitudes and add their angles.

Explore the conversion between polar and rectangular forms of complex numbers z0 ≈ 0.6687∠(−0.0899) and z1 ≈ 0.6687∠3.0517. Learn about the modulus and argument, and how to express these numbers in both forms. Suitable for advanced mathematics students.

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