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The problem asks to simplify the expression and write the answer in the form \( a + bi \). The expression given is:

\[
-\left(\frac{1 + 9i}{4}\right) + \frac{7}{3} - \frac{10 - 2i}{3}
\]

### Step 1: Simplify Each Term

1. **First Term:**
   \[
   -\left(\frac{1 + 9i}{4}\right) = -\frac{1 + 9i}{4} = -\frac{1}{4} - \frac{9i}{4}
   \]

2. **Second Term:**
   \[
   \frac{7}{3}
   \]
   This term is already in its simplest form.

3. **Third Term:**
   \[
   \frac{10 - 2i}{3} = \frac{10}{3} - \frac{2i}{3}
   \]

### Step 2: Combine the Real Parts
Add the real parts together:
\[
-\frac{1}{4} + \frac{7}{3} - \frac{10}{3}
\]

To add these fractions, convert them to have a common denominator:

\[
-\frac{1}{4} + \frac{7}{3} - \frac{10}{3} = -\frac{1}{4} + \frac{7 - 10}{3} = -\frac{1}{4} - \frac{3}{3} = -\frac{1}{4} - 1
\]

Now, combine \(-\frac{1}{4}\) and \(-1\):

\[
-\frac{1}{4} - \frac{4}{4} = -\frac{5}{4}
\]

### Step 3: Combine the Imaginary Parts
Now, add the imaginary parts:
\[
-\frac{9i}{4} - \frac{2i}{3}
\]

To add these fractions, convert them to have a common denominator:

\[
-\frac{9i}{4} - \frac{2i}{3} = -\frac{27i}{12} - \frac{8i}{12} = -\frac{35i}{12}
\]

### Final Answer

So the expression simplifies to:

\[
-\frac{5}{4} - \frac{35i}{12}
\]

This is already in the form \( a + bi \) where \( a = -\frac{5}{4} \) and \( b = -\frac{35}{12} \).

Would you like any additional details or have any questions?

Here are some related questions:
1. How do you multiply complex numbers?
2. What are the different ways to represent complex numbers?
3. How do you find the magnitude of a complex number?
4. What is the polar form of a complex number?
5. How do you divide complex numbers?

**Tip:** When working with complex numbers, always separate the real and imaginary parts to simplify the calculations.

-(1 + 9i)/4 + 7/3 - (10 - 2i)/3. Simplify and write the answer in the form a + bi.

This problem simplifies complex fractions and expresses the result in the standard a + bi form, involving key concepts like addition of complex numbers and fractions. Suitable for students in Grades 9-12.

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