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Let's simplify the given expression step by step.

The expression is:
\[
-\sqrt{121} + \sqrt{-75} - \sqrt{81} - \sqrt{-192}
\]

### Step 1: Simplify the real square roots.
- \(\sqrt{121} = 11\)
- \(\sqrt{81} = 9\)

Thus, the expression becomes:
\[
-11 + \sqrt{-75} - 9 - \sqrt{-192}
\]

### Step 2: Simplify the imaginary square roots.
For imaginary numbers, we use the property: \(\sqrt{-x} = i\sqrt{x}\), where \(i\) is the imaginary unit.

- \(\sqrt{-75} = i\sqrt{75} = i \times \sqrt{25 \times 3} = 5i\sqrt{3}\)
- \(\sqrt{-192} = i\sqrt{192} = i \times \sqrt{64 \times 3} = 8i\sqrt{3}\)

Now the expression becomes:
\[
-11 + 5i\sqrt{3} - 9 - 8i\sqrt{3}
\]

### Step 3: Combine like terms.
- Combine the real terms: \(-11 - 9 = -20\)
- Combine the imaginary terms: \(5i\sqrt{3} - 8i\sqrt{3} = -3i\sqrt{3}\)

Thus, the simplified expression in \(a + bi\) form is:
\[
-20 - 3i\sqrt{3}
\]

Would you like more details or have any further questions?

Here are five related questions for further practice:
1. How would you simplify \(\sqrt{-49} + \sqrt{100} - \sqrt{-25}\)?
2. How do you handle square roots of negative numbers when simplifying expressions?
3. What is the general form of a complex number, and how do you interpret it geometrically?
4. How do you add and subtract complex numbers?
5. Can you represent \(-20 - 3i\sqrt{3}\) on the complex plane?

**Tip:** When simplifying square roots of negative numbers, always express them in terms of \(i\) (the imaginary unit), and simplify the square root of the positive part separately.

Simplify the expression to a + bi form: -√121 + √-75 - √81 - √-192

Learn how to simplify the expression -√121 + √-75 - √81 - √-192 to the form a + bi. This solution involves key concepts in complex numbers and imaginary units, suitable for high school students (Grades 9-12).

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