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To simplify the given expression into the form \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part, let's break down the terms.

The expression is:

\[
\sqrt{121} + \sqrt{-49} + \sqrt{64} - \sqrt{-81}
\]

### Step-by-Step Simplification:
1. **Simplify each square root term:**
   - \( \sqrt{121} = 11 \) (since \( 11^2 = 121 \))
   - \( \sqrt{-49} = \sqrt{49} \cdot \sqrt{-1} = 7i \) (since \( \sqrt{-1} = i \))
   - \( \sqrt{64} = 8 \) (since \( 8^2 = 64 \))
   - \( \sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = 9i \)

2. **Substitute these values into the original expression:**
   \[
   11 + 7i + 8 - 9i
   \]

3. **Combine the real and imaginary parts:**
   - Real part: \( 11 + 8 = 19 \)
   - Imaginary part: \( 7i - 9i = -2i \)

### Final answer:
The simplified expression in \( a + bi \) form is:

\[
19 - 2i
\]

Let me know if you'd like any further details or have questions!

Here are five related questions to expand your understanding:
1. How do you handle complex numbers involving cube roots instead of square roots?
2. What happens if there's no imaginary part in a complex number expression?
3. How can you plot complex numbers on the complex plane?
4. What are the rules for multiplying two complex numbers?
5. How does Euler's formula relate to complex numbers?

**Tip:** Always remember that \( \sqrt{-1} = i \), which is the fundamental property of imaginary numbers!

Simplify the expression to a + bi form: √121 + √-49 + √64 - √-81

Simplify complex expressions like √121 + √-49 + √64 - √-81 into a + bi form. Learn how to handle square roots of negative numbers, apply the imaginary unit, and combine real and imaginary terms for accurate solutions. Suitable for Grades 9-12 students.

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