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The image contains two problems involving complex numbers. Let's solve them step by step.

### Problem 6:
\[
(7 - 20i) + (-30i + 6i)
\]

#### Solution:
1. **Combine the real parts:**  
   The real part is \( 7 \) (since there is no real part in \(-30i + 6i\)).
   
2. **Combine the imaginary parts:**  
   The imaginary part is \( -20i + (-30i + 6i) \).  
   First, simplify the expression inside the parentheses:  
   \[
   -30i + 6i = -24i
   \]  
   Now, add it to \(-20i\):  
   \[
   -20i + (-24i) = -44i
   \]
   
3. **Final Answer:**  
   The result is \( 7 - 44i \).

### Problem 7:
\[
[7 - (30 - 15i + 6i)](3i + 3)
\]

#### Solution:
1. **Simplify inside the parentheses:**  
   First, simplify \(30 - 15i + 6i\):  
   \[
   -15i + 6i = -9i
   \]  
   So, we have:  
   \[
   7 - (30 - 9i)
   \]  
   Distribute the negative sign:
   \[
   7 - 30 + 9i = -23 + 9i
   \]
   
2. **Expand the multiplication:**  
   Multiply \((-23 + 9i)\) by \((3i + 3)\):  
   \[
   (-23 + 9i)(3i + 3)
   \]  
   Use the distributive property:
   \[
   = -23(3i) + -23(3) + 9i(3i) + 9i(3)
   \]
   \[
   = -69i - 69 + 27i^2 + 27i
   \]
   
   Remember that \(i^2 = -1\):
   \[
   = -69i - 69 + 27(-1) + 27i
   \]
   Simplify the expression:
   \[
   = -69 - 27 + (-69i + 27i)
   \]
   Combine like terms:
   \[
   = -96 - 42i
   \]
   
3. **Final Answer:**  
   The result is \(-96 - 42i\).

---

Would you like more details or have any questions about these problems? 

### Related Questions:
1. How do you multiply two complex numbers in general?
2. What is the significance of the imaginary unit \(i\)?
3. How do you simplify complex expressions with multiple terms?
4. What is the geometric interpretation of complex numbers?
5. How can you represent complex numbers on a graph?

### Tip:
Always remember that when multiplying complex numbers, \(i^2 = -1\) is key to simplifying the expression!

Learn how to solve complex number problems step-by-step. This detailed explanation covers arithmetic operations with complex numbers, including addition, subtraction, and multiplication. Suitable for advanced high school students.

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