Evaluate:
(i) `x^(2)+4x+7` when `x=2+sqrt(-3)`
(ii) `2x^(3)-9x^(2)-10x+13` when `x=3+sqrt(-5)`

Answer

Let's solve the given problems step by step.

### Part (i): Evaluate \( x^2 + 4x + 7 \) when \( x = 2 + \sqrt{-3} \)

1. **Substitute the value of \( x \)**:
\[ x = 2 + \sqrt{-3} = 2 + i\sqrt{3} \]
Therefore, we need to evaluate:
\[ (2 + i\sqrt{3})^2 + 4(2 + i\sqrt{3}) + 7 \]

2. **Calculate \( (2 + i\sqrt{3})^2 \)**:
\[ (2 + i\sqrt{3})^2 = 2^2 + 2 \cdot 2 \cdot i\sqrt{3} + (i\sqrt{3})^2 \]
\[ = 4 + 4i\sqrt{3} + (-3) = 1 + 4i\sqrt{3} \]

3. **Calculate \( 4(2 + i\sqrt{3}) \)**:
\[ 4(2 + i\sqrt{3}) = 8 + 4i\sqrt{3} \]

4. **Combine all parts**:
\[ (1 + 4i\sqrt{3}) + (8 + 4i\sqrt{3}) + 7 \]
\[ = 1 + 8 + 7 + 4i\sqrt{3} + 4i\sqrt{3} = 16 + 8i\sqrt{3} \]

5. **Final result for part (i)**:
\[ x^2 + 4x + 7 = 16 + 8i\sqrt{3} \]

### Part (ii): Evaluate \( 2x^3 - 9x^2 - 10x + 13 \) when \( x = 3 + \sqrt{-5} \)

1. **Substitute the value of \( x \)**:
\[ x = 3 + \sqrt{-5} = 3 + i\sqrt{5} \]
Therefore, we need to evaluate:
\[ 2(3 + i\sqrt{5})^3 - 9(3 + i\sqrt{5})^2 - 10(3 + i\sqrt{5}) + 13 \]

2. **Calculate \( (3 + i\sqrt{5})^2 \)**:
\[ (3 + i\sqrt{5})^2 = 3^2 + 2 \cdot 3 \cdot i\sqrt{5} + (i\sqrt{5})^2 \]
\[ = 9 + 6i\sqrt{5} - 5 = 4 + 6i\sqrt{5} \]

3. **Calculate \( (3 + i\sqrt{5})^3 \)**:
Using the formula \( (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \):
\[ = 3^3 + 3 \cdot 3^2 \cdot i\sqrt{5} + 3 \cdot 3 \cdot (i\sqrt{5})^2 + (i\sqrt{5})^3 \]
\[ = 27 + 27i\sqrt{5} - 15i\sqrt{5} - 5i\sqrt{5} = 27 + 12i\sqrt{5} - 5 \]
\[ = 22 + 12i\sqrt{5} \]

4. **Calculate \( 2(3 + i\sqrt{5})^3 \)**:
\[ 2(22 + 12i\sqrt{5}) = 44 + 24i\sqrt{5} \]

5. **Calculate \( -9(3 + i\sqrt{5})^2 \)**:
\[ -9(4 + 6i\sqrt{5}) = -36 - 54i\sqrt{5} \]

6. **Calculate \( -10(3 + i\sqrt{5}) \)**:
\[ -10(3 + i\sqrt{5}) = -30 - 10i\sqrt{5} \]

7. **Combine all parts**:
\[ (44 + 24i\sqrt{5}) + (-36 - 54i\sqrt{5}) + (-30 - 10i\sqrt{5}) + 13 \]
\[ = (44 - 36 - 30 + 13) + (24i\sqrt{5} - 54i\sqrt{5} - 10i\sqrt{5}) \]
\[ = -9 - 40i\sqrt{5} \]

8. **Final result for part (ii)**:
\[ 2x^3 - 9x^2 - 10x + 13 = -9 - 40i\sqrt{5} \]

### Summary of Results:
- Part (i): \( 16 + 8i\sqrt{3} \)
- Part (ii): \( -9 - 40i\sqrt{5} \)