Simplify The Expression: { -8i - 7i$}$

Introduction

In mathematics, simplifying expressions is a crucial step in solving problems and understanding complex concepts. When dealing with algebraic expressions, combining like terms is a fundamental technique used to simplify expressions. In this article, we will focus on simplifying the expression $-8i - 7i$, where $i$ is the imaginary unit. We will explore the concept of like terms, the properties of imaginary numbers, and the steps involved in simplifying the given expression.

Understanding Like Terms

Like terms are algebraic expressions that have the same variable raised to the same power. In the expression $-8i - 7i$, both terms have the variable $i$ raised to the power of 1. Therefore, they are like terms, and we can combine them using the rules of arithmetic.

Properties of Imaginary Numbers

Imaginary numbers are a fundamental concept in mathematics, and they play a crucial role in algebra and calculus. The imaginary unit $i$ is defined as the square root of $-1$, denoted by $i = \sqrt{-1}$. This means that $i^2 = -1$. Imaginary numbers have several properties that are essential to understand when working with expressions like $-8i - 7i$.

Simplifying the Expression

To simplify the expression $-8i - 7i$, we need to combine the like terms. We can do this by adding the coefficients of the like terms. In this case, the coefficients are $-8$ and $-7$. When we add these coefficients, we get:

$$-8i - 7i = (-8 + (-7))i$$

Using the rules of arithmetic, we can simplify the expression further:

$$(-8 + (-7))i = (-15)i$$

Therefore, the simplified expression is $-15i$.

Conclusion

Simplifying expressions is an essential skill in mathematics, and it requires a deep understanding of algebraic concepts, including like terms and imaginary numbers. In this article, we have explored the concept of like terms, the properties of imaginary numbers, and the steps involved in simplifying the expression $-8i - 7i$. By combining like terms and applying the rules of arithmetic, we have arrived at the simplified expression $-15i$. This example demonstrates the importance of simplifying expressions in mathematics and highlights the need for a thorough understanding of algebraic concepts.

Frequently Asked Questions

• What are like terms in algebra? Like terms are algebraic expressions that have the same variable raised to the same power.
• What is the imaginary unit $i$? The imaginary unit $i$ is defined as the square root of $-1$, denoted by $i = \sqrt{-1}$.
• How do you simplify an expression with like terms? To simplify an expression with like terms, you need to combine the coefficients of the like terms using the rules of arithmetic.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Imaginary Numbers

Final Thoughts

Simplifying expressions is a fundamental skill in mathematics, and it requires a deep understanding of algebraic concepts, including like terms and imaginary numbers. By combining like terms and applying the rules of arithmetic, we can simplify expressions and arrive at the correct solution. In this article, we have explored the concept of like terms, the properties of imaginary numbers, and the steps involved in simplifying the expression $-8i - 7i$. We hope that this example has demonstrated the importance of simplifying expressions in mathematics and highlighted the need for a thorough understanding of algebraic concepts.

Introduction

In our previous article, we explored the concept of simplifying expressions, focusing on the expression $-8i - 7i$. We discussed the importance of understanding like terms and the properties of imaginary numbers in simplifying expressions. In this article, we will provide a Q&A section to address common questions and concerns related to simplifying expressions.

Q&A

Q: What are like terms in algebra?

A: Like terms are algebraic expressions that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: What is the imaginary unit $i$?

A: The imaginary unit $i$ is defined as the square root of $-1$, denoted by $i = \sqrt{-1}$. This means that $i^2 = -1$.

Q: How do you simplify an expression with like terms?

A: To simplify an expression with like terms, you need to combine the coefficients of the like terms using the rules of arithmetic. For example, in the expression $-8i - 7i$, we can combine the coefficients by adding $-8$ and $-7$ to get $-15i$.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not combining like terms
• Not applying the rules of arithmetic correctly
• Not checking for errors in the expression

Q: How do you check for errors in an expression?

A: To check for errors in an expression, you can:

• Simplify the expression using the rules of arithmetic
• Check if the expression is in its simplest form
• Verify that the expression is correct by plugging in values or using a calculator

Q: What are some real-world applications of simplifying expressions?

A: Simplifying expressions has many real-world applications, including:

• Solving equations and inequalities
• Graphing functions
• Calculating areas and volumes of shapes
• Modeling real-world phenomena

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by:

• Working through algebraic exercises and problems
• Using online resources and tools, such as calculators and software
• Joining study groups or seeking help from a tutor or teacher

Conclusion

Simplifying expressions is a fundamental skill in mathematics, and it requires a deep understanding of algebraic concepts, including like terms and imaginary numbers. By combining like terms and applying the rules of arithmetic, we can simplify expressions and arrive at the correct solution. In this article, we have provided a Q&A section to address common questions and concerns related to simplifying expressions. We hope that this article has been helpful in clarifying the concept of simplifying expressions and providing guidance on how to practice and apply this skill.

Frequently Asked Questions

• What are some common mistakes to avoid when simplifying expressions?
• How do you check for errors in an expression?
• What are some real-world applications of simplifying expressions?
• How can I practice simplifying expressions?

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Imaginary Numbers

Final Thoughts

Simplifying expressions is a crucial skill in mathematics, and it requires a deep understanding of algebraic concepts, including like terms and imaginary numbers. By combining like terms and applying the rules of arithmetic, we can simplify expressions and arrive at the correct solution. We hope that this article has been helpful in clarifying the concept of simplifying expressions and providing guidance on how to practice and apply this skill.