Evaluate The Expression: − ( − 9 ) 2 = ? \sqrt{-(-9)^2}=\text{ ?} − ( − 9 ) 2 ​ = ? (Note: I = − 1 I=\sqrt{-1} I = − 1 ​ )A. 9 I 9i 9 I B. 9 + I 9+i 9 + I C. 9 − I 9-i 9 − I D. 9 E. − 9 -9 − 9

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Introduction

In this article, we will evaluate the expression $\sqrt{-(-9)^2}$ using the given information that $i=\sqrt{-1}$. We will break down the expression step by step and provide a clear explanation of each step.

Understanding the Expression

The expression $\sqrt{-(-9)^2}$ can be broken down into two parts: $\sqrt{-1}$ and $(-9)^2$. We know that $i=\sqrt{-1}$, so we can substitute this value into the expression. The second part, $(-9)^2$, is a simple exponentiation that can be evaluated as $81$.

Evaluating the Expression

Now that we have broken down the expression into two parts, we can evaluate it step by step.

Step 1: Evaluate $(-9)^2$

$(-9)^2 = 81$

Step 2: Substitute $i$ for $\sqrt{-1}$

$\sqrt{-1} = i$

Step 3: Evaluate the expression $\sqrt{-(-9)^2}$

$\sqrt{-(-9)^2} = \sqrt{-81} = \sqrt{-1} \cdot \sqrt{81} = i \cdot 9 = 9i$

Conclusion

Based on the step-by-step evaluation of the expression, we can conclude that $\sqrt{-(-9)^2} = 9i$.

Comparison with Answer Choices

Now that we have evaluated the expression, we can compare our answer with the answer choices provided.

• A. $9i$ - This is the correct answer.
• B. $9+i$ - This is not the correct answer.
• C. $9-i$ - This is not the correct answer.
• D. 9 - This is not the correct answer.
• E. $-9$ - This is not the correct answer.

Final Answer

The final answer is $\boxed{9i}$.

Understanding the Concept of Imaginary Numbers

Imaginary numbers are a fundamental concept in mathematics that can be used to extend the real number system. They are defined as the square root of a negative number. In this article, we used the concept of imaginary numbers to evaluate the expression $\sqrt{-(-9)^2}$.

The Importance of Imaginary Numbers

Imaginary numbers have many applications in mathematics and science. They are used to solve equations that involve the square root of a negative number. They are also used in the study of complex numbers, which are numbers that have both real and imaginary parts.

Conclusion

In conclusion, we have evaluated the expression $\sqrt{-(-9)^2}$ using the concept of imaginary numbers. We have shown that the correct answer is $9i$. We have also discussed the importance of imaginary numbers in mathematics and science.

References

• [1] "Imaginary Numbers" by Math Open Reference. Retrieved 2023-12-01.
• [2] "Complex Numbers" by Khan Academy. Retrieved 2023-12-01.

Additional Resources

• [1] "Imaginary Numbers" by Wolfram MathWorld. Retrieved 2023-12-01.
• [2] "Complex Numbers" by MIT OpenCourseWare. Retrieved 2023-12-01.
  Evaluating the Expression: $\sqrt{-(-9)^2}$ - Q&A =====================================================

Introduction

In our previous article, we evaluated the expression $\sqrt{-(-9)^2}$ using the concept of imaginary numbers. We showed that the correct answer is $9i$. In this article, we will provide a Q&A section to help clarify any doubts or questions that readers may have.

Q&A

Q: What is the concept of imaginary numbers?

A: Imaginary numbers are a fundamental concept in mathematics that can be used to extend the real number system. They are defined as the square root of a negative number.

Q: Why do we need imaginary numbers?

A: Imaginary numbers are used to solve equations that involve the square root of a negative number. They are also used in the study of complex numbers, which are numbers that have both real and imaginary parts.

Q: How do we evaluate the expression $\sqrt{-(-9)^2}$?

A: To evaluate the expression $\sqrt{-(-9)^2}$, we need to break it down into two parts: $\sqrt{-1}$ and $(-9)^2$. We know that $i=\sqrt{-1}$, so we can substitute this value into the expression. The second part, $(-9)^2$, is a simple exponentiation that can be evaluated as $81$.

Q: What is the final answer to the expression $\sqrt{-(-9)^2}$?

A: The final answer to the expression $\sqrt{-(-9)^2}$ is $9i$.

Q: Why is the answer $9i$ and not $9$ or $-9$?

A: The answer $9i$ is correct because we are evaluating the expression $\sqrt{-(-9)^2}$, which involves the square root of a negative number. The square root of a negative number is an imaginary number, which is represented by $i$. Therefore, the correct answer is $9i$.

Q: What are some real-world applications of imaginary numbers?

A: Imaginary numbers have many applications in mathematics and science. They are used to solve equations that involve the square root of a negative number. They are also used in the study of complex numbers, which are numbers that have both real and imaginary parts.

Q: Can you provide some examples of complex numbers?

A: Yes, some examples of complex numbers are:

• $3+4i$
• $2-3i$
• $5+2i$

Q: How do we add and subtract complex numbers?

A: To add and subtract complex numbers, we need to add or subtract the real parts and the imaginary parts separately. For example:

• $(3+4i) + (2-3i) = (3+2) + (4-3)i = 5+i$
• $(3+4i) - (2-3i) = (3-2) + (4+3)i = 1+7i$

Conclusion

In conclusion, we have provided a Q&A section to help clarify any doubts or questions that readers may have about the expression $\sqrt{-(-9)^2}$. We have shown that the correct answer is $9i$ and have discussed the importance of imaginary numbers in mathematics and science.

References

• [1] "Imaginary Numbers" by Math Open Reference. Retrieved 2023-12-01.
• [2] "Complex Numbers" by Khan Academy. Retrieved 2023-12-01.

Additional Resources

• [1] "Imaginary Numbers" by Wolfram MathWorld. Retrieved 2023-12-01.
• [2] "Complex Numbers" by MIT OpenCourseWare. Retrieved 2023-12-01.