To solve this, let's simplify the expression step by step:

The expression is: $(-3 + 3i) + (6 + 2i) - (7 + 4i)$

Step 1: Distribute and Remove Parentheses

$= -3 + 3i + 6 + 2i - 7 - 4i$

Step 2: Combine Real Parts

Combine $-3$, $6$, and $-7$: $-3 + 6 - 7 = -4$

Step 3: Combine Imaginary Parts

Combine $3i$, $2i$, and $-4i$: $3i + 2i - 4i = i$

Final Answer

After combining, we get: $-4 + i$

The correct answer is: a) -4 + i

Would you like more details on any step or have further questions?

Related Questions

1. How do you add and subtract complex numbers in general?
2. What does the imaginary unit $i$ represent in mathematics?
3. How do you distribute terms when there are negative signs outside parentheses?
4. Can complex numbers be represented graphically? If so, how?
5. How would this problem change if we had multiplication between complex numbers?

Tip

When simplifying expressions with complex numbers, handle real and imaginary parts separately to avoid confusion.