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!