Compute: (i) `sqrt(-49)(2+sqrt(-9))`
(ii) `[2+sqrt(-25)]-[3-sqrt(-16)]+[1-sqrt(-9)]`.

Answer

Let's solve the given problems step by step.

### Part (i): Compute \( \sqrt{-49}(2+\sqrt{-9}) \)

1. **Identify the components**:
- We have \( \sqrt{-49} \) and \( 2 + \sqrt{-9} \).

2. **Compute \( \sqrt{-49} \)**:
- Using the property \( \sqrt{-x} = i \sqrt{x} \):
\[ \sqrt{-49} = i \sqrt{49} = i \cdot 7 = 7i \]

3. **Compute \( \sqrt{-9} \)**:
- Similarly,
\[ \sqrt{-9} = i \sqrt{9} = i \cdot 3 = 3i \]

4. **Substitute back into the expression**:
- Now substitute \( \sqrt{-49} \) and \( \sqrt{-9} \) back into the expression:
\[ \sqrt{-49}(2+\sqrt{-9}) = 7i(2 + 3i) \]

5. **Distribute \( 7i \)**:
- Distributing \( 7i \):
\[ 7i \cdot 2 + 7i \cdot 3i = 14i + 21i^2 \]

6. **Simplify \( 21i^2 \)**:
- Since \( i^2 = -1 \):
\[ 21i^2 = 21(-1) = -21 \]

7. **Combine the real and imaginary parts**:
- Thus, we have:
\[ -21 + 14i \]

### Final Result for Part (i):
\[ \sqrt{-49}(2+\sqrt{-9}) = -21 + 14i \]

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### Part (ii): Compute \( [2+\sqrt{-25}] - [3-\sqrt{-16}] + [1-\sqrt{-9}] \)

1. **Identify the components**:
- We have three terms: \( 2 + \sqrt{-25} \), \( 3 - \sqrt{-16} \), and \( 1 - \sqrt{-9} \).

2. **Compute \( \sqrt{-25} \)**:
- Using the property \( \sqrt{-x} = i \sqrt{x} \):
\[ \sqrt{-25} = i \sqrt{25} = i \cdot 5 = 5i \]

3. **Compute \( \sqrt{-16} \)**:
- Similarly,
\[ \sqrt{-16} = i \sqrt{16} = i \cdot 4 = 4i \]

4. **Compute \( \sqrt{-9} \)**:
- And,
\[ \sqrt{-9} = i \sqrt{9} = i \cdot 3 = 3i \]

5. **Substitute back into the expression**:
- Now substitute:
\[ [2 + 5i] - [3 - 4i] + [1 - 3i] \]

6. **Distribute the negative sign**:
- Distributing the negative sign:
\[ 2 + 5i - 3 + 4i + 1 - 3i \]

7. **Combine the real parts**:
- Combine the real parts:
\[ 2 - 3 + 1 = 0 \]

8. **Combine the imaginary parts**:
- Combine the imaginary parts:
\[ 5i + 4i - 3i = 6i \]

### Final Result for Part (ii):
\[ [2+\sqrt{-25}] - [3-\sqrt{-16}] + [1-\sqrt{-9}] = 0 + 6i = 6i \]

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