Evaluate { (2-5i)(p+q)(i)$}$ When { P=2$}$ And { Q=5i$}$.A. ${ 29i\$} B. ${ 29i-20\$} C. { -21i$}$ D. 29

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Introduction

In this article, we will delve into the world of complex numbers and expressions. We will evaluate the expression {(2-5i)(p+q)(i)$}$ when {p=2$}$ and {q=5i$}$. This involves substituting the given values of {p$}$ and {q$}$ into the expression and simplifying it to obtain the final result.

Understanding Complex Numbers

Before we proceed, let's briefly review the basics of complex numbers. 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 {b$}$.

Substituting Values into the Expression

Now, let's substitute the given values of {p$}$ and {q$}$ into the expression {(2-5i)(p+q)(i)$}$. We have {p=2$}$ and {q=5i$}$. Substituting these values, we get:

{(2-5i)(2+5i)(i)$}$

Expanding the Expression

To simplify the expression, we need to expand it. We can do this by multiplying the terms together. Let's start by multiplying the first two terms:

{(2-5i)(2+5i)$]

Using the distributive property, we get:

[$2(2+5i)-5i(2+5i)$]

Expanding further, we get:

[$4+10i-10i-25i^2$]

Since [i^2=-1\$}, we can simplify the expression to:

${$4+25$]

Combining like terms, we get:

[29\$}

Multiplying by {i$}$

Now, let's multiply the result by {i$}$:

${29i\$}

Conclusion

In conclusion, we have evaluated the expression {(2-5i)(p+q)(i)$}$ when {p=2$}$ and {q=5i$}$. By substituting the given values and simplifying the expression, we obtained the final result of ${29i\$}.

Answer

The correct answer is:

  • A. ${29i\$}

Discussion

This problem involves evaluating a complex expression involving complex numbers. The key steps involved in solving this problem are substituting the given values into the expression, expanding the expression, and simplifying it to obtain the final result. This problem requires a good understanding of complex numbers and expressions, as well as the ability to apply mathematical operations to simplify the expression.

Additional Tips and Resources

  • To evaluate complex expressions, it's essential to follow the order of operations (PEMDAS/BODMAS) and to simplify the expression step-by-step.
  • When working with complex numbers, it's crucial to remember that {i^2=-1$}$.
  • For more practice problems and resources on complex numbers and expressions, check out the following websites:
    • Khan Academy: Complex Numbers
    • Mathway: Complex Numbers
    • Wolfram Alpha: Complex Numbers

Final Thoughts

Introduction

In our previous article, we evaluated the expression {(2-5i)(p+q)(i)$}$ when {p=2$}$ and {q=5i$}$. We obtained the final result of ${29i\$}. In this article, we will provide a Q&A guide to help you better understand complex expressions and how to evaluate them.

Q: What is a complex expression?

A: A complex expression is an expression that involves complex numbers, which are numbers 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$}$.

Q: How do I evaluate a complex expression?

A: To evaluate a complex expression, you need to follow the order of operations (PEMDAS/BODMAS) and simplify the expression step-by-step. This involves substituting the given values into the expression, expanding the expression, and simplifying it to obtain the final result.

Q: What is the order of operations (PEMDAS/BODMAS)?

A: The order of operations (PEMDAS/BODMAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS/BODMAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify a complex expression?

A: To simplify a complex expression, you need to combine like terms and eliminate any unnecessary operations. This involves using the distributive property, combining like terms, and simplifying the expression to obtain the final result.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows you to multiply a single term by multiple terms. It states that for any numbers {a$}$, {b$}$, and {c$}$, the following equation holds:

{a(b+c)=ab+ac$}$

Q: How do I use the distributive property to simplify a complex expression?

A: To use the distributive property to simplify a complex expression, you need to multiply each term in the expression by the other terms. This involves using the distributive property to expand the expression and then combining like terms to simplify it.

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

A: Some common mistakes to avoid when evaluating complex expressions include:

  • Not following the order of operations (PEMDAS/BODMAS).
  • Not simplifying the expression step-by-step.
  • Not combining like terms.
  • Not eliminating unnecessary operations.

Q: How can I practice evaluating complex expressions?

A: You can practice evaluating complex expressions by working through practice problems and exercises. You can also use online resources, such as Khan Academy, Mathway, and Wolfram Alpha, to help you practice and improve your skills.

Conclusion

Evaluating complex expressions can be a challenging task, but with practice and a good understanding of complex numbers and expressions, it becomes more manageable. By following the steps outlined in this article and avoiding common mistakes, you can evaluate complex expressions with confidence and accuracy.

Additional Tips and Resources

  • To evaluate complex expressions, it's essential to follow the order of operations (PEMDAS/BODMAS) and to simplify the expression step-by-step.
  • When working with complex numbers, it's crucial to remember that {i^2=-1$}$.
  • For more practice problems and resources on complex numbers and expressions, check out the following websites:
    • Khan Academy: Complex Numbers
    • Mathway: Complex Numbers
    • Wolfram Alpha: Complex Numbers

Final Thoughts

Evaluating complex expressions is an essential skill in mathematics, and with practice and patience, you can master it. By following the steps outlined in this article and avoiding common mistakes, you can evaluate complex expressions with confidence and accuracy.