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The problem you provided is to subtract and simplify the following expression:

\[
(6 - 3i) - (-3 + i)
\]

### Step-by-step solution:

1. Distribute the negative sign across the second set of parentheses:
   \[
   (6 - 3i) - (-3 + i) = 6 - 3i + 3 - i
   \]

2. Combine the real and imaginary parts separately:
   - Real part: \(6 + 3 = 9\)
   - Imaginary part: \(-3i - i = -4i\)

So, the simplified expression is:

\[
9 - 4i
\]

### Final Answer:
\[
9 - 4i
\]

Would you like further details or have any other questions? Here are some related questions to expand your understanding:

1. How do you add or subtract two complex numbers in general?
2. What are the real and imaginary components of a complex number?
3. How would you simplify \((a + bi) - (c + di)\)?
4. Can you represent the result geometrically on the complex plane?
5. How does multiplication of complex numbers differ from addition?

**Tip:** Always group the real and imaginary parts separately when adding or subtracting complex numbers.

Learn how to subtract complex numbers with this example: (6 - 3i) - (-3 + i). Understand how to combine real and imaginary parts to get the solution 9 - 4i. Suitable for high school students studying algebra.

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