Simplify The Expression To \[$a + Bi\$\] Form:\[$(6 - 4i) + (5 + 3i)\$\]

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Introduction

In mathematics, the process of simplifying complex expressions is a crucial skill that helps us to solve problems efficiently. When dealing with complex numbers, we often need to add or subtract them, which can be a bit tricky. In this article, we will focus on simplifying the expression {(6 - 4i) + (5 + 3i)$}$ to the form {a + bi$}$. We will break down the steps involved in this process and provide a clear explanation of each step.

Understanding Complex Numbers

Before we dive into simplifying the expression, let's quickly review what complex numbers are. A complex number is a number that can be expressed in the form {a + bi$}$, where {a$}$ and {b$}$ are real numbers, and {i$}$ is the imaginary unit, which satisfies the equation {i^2 = -1$}$. The real part of a complex number is {a$}$, and the imaginary part is {bi$}$.

Adding Complex Numbers

To simplify the expression {(6 - 4i) + (5 + 3i)$}$, we need to add the real parts and the imaginary parts separately. When adding complex numbers, we add the real parts together and the imaginary parts together.

Step 1: Add the Real Parts

The real part of the first complex number is ${6\$}, and the real part of the second complex number is ${5\$}. To add these two real numbers, we simply add them together:

${6 + 5 = 11\$}

Step 2: Add the Imaginary Parts

The imaginary part of the first complex number is {-4i$}$, and the imaginary part of the second complex number is ${3i\$}. To add these two imaginary numbers, we simply add them together:

{-4i + 3i = -i$}$

Step 3: Combine the Real and Imaginary Parts

Now that we have added the real and imaginary parts separately, we can combine them to form the simplified expression:

${11 + (-i)\$}

Simplifying the Expression

The expression ${11 + (-i)\$} can be simplified further by removing the negative sign from the imaginary part. When we remove the negative sign, the expression becomes:

${11 - i\$}

Conclusion

In this article, we simplified the expression {(6 - 4i) + (5 + 3i)$}$ to the form {a + bi$}$. We broke down the steps involved in this process and provided a clear explanation of each step. By following these steps, we can simplify complex expressions and solve problems efficiently.

Frequently Asked Questions

• What is the simplified form of the expression {(6 - 4i) + (5 + 3i)$}$?
• How do we add complex numbers?
• What is the difference between adding real numbers and adding imaginary numbers?

Answers

• The simplified form of the expression {(6 - 4i) + (5 + 3i)$}$ is ${11 - i\$}.
• We add complex numbers by adding the real parts together and the imaginary parts together.
• The difference between adding real numbers and adding imaginary numbers is that we add the real parts together and the imaginary parts together separately.

Final Thoughts

Simplifying complex expressions is an essential skill in mathematics, and it requires practice and patience. By following the steps outlined in this article, you can simplify complex expressions and solve problems efficiently. Remember to always add the real parts together and the imaginary parts together separately, and don't forget to remove the negative sign from the imaginary part when necessary. With practice and persistence, you will become proficient in simplifying complex expressions and solving problems in mathematics.

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Introduction

In our previous article, we simplified the expression {(6 - 4i) + (5 + 3i)$}$ to the form {a + bi$}$. We broke down the steps involved in this process and provided a clear explanation of each step. In this article, we will answer some frequently asked questions related to simplifying complex expressions.

Q&A

Q: What is the simplified form of the expression {(6 - 4i) + (5 + 3i)$}$?

A: The simplified form of the expression {(6 - 4i) + (5 + 3i)$}$ is ${11 - i\$}.

Q: How do we add complex numbers?

A: We add complex numbers by adding the real parts together and the imaginary parts together separately.

Q: What is the difference between adding real numbers and adding imaginary numbers?

A: The difference between adding real numbers and adding imaginary numbers is that we add the real parts together and the imaginary parts together separately.

Q: Can we simplify complex expressions with negative real parts?

A: Yes, we can simplify complex expressions with negative real parts. When we simplify a complex expression with a negative real part, we simply remove the negative sign from the real part.

Q: Can we simplify complex expressions with negative imaginary parts?

A: Yes, we can simplify complex expressions with negative imaginary parts. When we simplify a complex expression with a negative imaginary part, we simply remove the negative sign from the imaginary part.

Q: How do we subtract complex numbers?

A: We subtract complex numbers by subtracting the real parts together and the imaginary parts together separately.

Q: What is the difference between subtracting real numbers and subtracting imaginary numbers?

A: The difference between subtracting real numbers and subtracting imaginary numbers is that we subtract the real parts together and the imaginary parts together separately.

Q: Can we simplify complex expressions with fractions?

A: Yes, we can simplify complex expressions with fractions. When we simplify a complex expression with a fraction, we simply multiply the numerator and denominator by the conjugate of the denominator.

Q: Can we simplify complex expressions with decimals?

A: Yes, we can simplify complex expressions with decimals. When we simplify a complex expression with a decimal, we simply round the decimal to the nearest whole number.

Conclusion

In this article, we answered some frequently asked questions related to simplifying complex expressions. We provided clear explanations and examples to help you understand the concepts. By following the steps outlined in this article, you can simplify complex expressions and solve problems efficiently.

Frequently Asked Questions

• What is the simplified form of the expression {(6 - 4i) + (5 + 3i)$}$?
• How do we add complex numbers?
• What is the difference between adding real numbers and adding imaginary numbers?
• Can we simplify complex expressions with negative real parts?
• Can we simplify complex expressions with negative imaginary parts?
• How do we subtract complex numbers?
• What is the difference between subtracting real numbers and subtracting imaginary numbers?
• Can we simplify complex expressions with fractions?
• Can we simplify complex expressions with decimals?

Answers

• The simplified form of the expression {(6 - 4i) + (5 + 3i)$}$ is ${11 - i\$}.
• We add complex numbers by adding the real parts together and the imaginary parts together separately.
• The difference between adding real numbers and adding imaginary numbers is that we add the real parts together and the imaginary parts together separately.
• Yes, we can simplify complex expressions with negative real parts.
• Yes, we can simplify complex expressions with negative imaginary parts.
• We subtract complex numbers by subtracting the real parts together and the imaginary parts together separately.
• The difference between subtracting real numbers and subtracting imaginary numbers is that we subtract the real parts together and the imaginary parts together separately.
• Yes, we can simplify complex expressions with fractions.
• Yes, we can simplify complex expressions with decimals.

Final Thoughts

Simplifying complex expressions is an essential skill in mathematics, and it requires practice and patience. By following the steps outlined in this article, you can simplify complex expressions and solve problems efficiently. Remember to always add the real parts together and the imaginary parts together separately, and don't forget to remove the negative sign from the imaginary part when necessary. With practice and persistence, you will become proficient in simplifying complex expressions and solving problems in mathematics.