Question: Perform indicated operations and write the answer in the $a + bi$ form.
$(4 + i) - (2 - 3i) - (3 - 2i)$
1. **State the problem:**
We need to simplify the expression $(4 + i) - (2 - 3i) - (3 - 2i)$ and write the result in the form $a + bi$.
2. **Recall the rule for subtraction of complex numbers:**
Subtract the real parts and the imaginary parts separately.
3. **Rewrite the expression by distributing the minus signs:**
$= (4 + i) - 2 + 3i - 3 + 2i$
4. **Group real and imaginary parts:**
Real parts: $4 - 2 - 3$
Imaginary parts: $i + 3i + 2i$
5. **Calculate the sums:**
Real: $4 - 2 - 3 = (4 - 2) - 3 = 2 - 3 = -1$
Imaginary: $1i + 3i + 2i = 6i$
6. **Write the final answer:**
$$-1 + 6i$$
Therefore, the answer is $-1 + 6i$.
7. **Match with options:**
Option (a) is $-1 + 6i$.
**Final answer:** (a) $-1 + 6i$