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Let's break down and solve the two given expressions, simplifying them into the form \( a + bi \) where \( a \) and \( b \) are real numbers and \( i \) is the imaginary unit.

### Part a: \( 4 + \sqrt{-49} \)

1. First, recognize that \( \sqrt{-49} \) can be rewritten as \( \sqrt{49} \times i = 7i \) because \( \sqrt{-1} = i \).
   
2. Now, simplify the expression:
   \[
   4 + 7i
   \]
   This is already in the form \( a + bi \), where \( a = 4 \) and \( b = 7 \).

### Part b: \( \frac{3 - 8i}{7} \)

1. Distribute the division over both terms in the numerator:
   \[
   \frac{3}{7} - \frac{8i}{7}
   \]
   
2. This expression is also already in the form \( a + bi \), where \( a = \frac{3}{7} \) and \( b = -\frac{8}{7} \).

### Final Answers:
- **a**: \( 4 + 7i \)
- **b**: \( \frac{3}{7} - \frac{8}{7}i \)

Would you like any further explanation on these steps? 

Here are 5 related questions for practice:
1. How do you simplify \( \sqrt{-16} \) into an imaginary number?
2. What is the complex form of \( 6 + \sqrt{-9} \)?
3. Can you simplify \( \frac{5 - 3i}{2} \)?
4. How do you add two complex numbers \( (3 + 4i) + (5 - 2i) \)?
5. What happens when you multiply \( i \times i \)?

**Tip:** When dealing with square roots of negative numbers, always factor out the imaginary unit \( i \) from the square root of the positive part.

Simplify each expression and write the result in the form a + bi: a. 4 + sqrt(-49), b. (3 - 8i) / 7

Learn how to simplify complex numbers involving square roots of negative numbers and division of complex numbers. This problem focuses on core concepts in imaginary and complex numbers and is ideal for high school students (Grades 9-12).

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