College

We appreciate your visit to Multiply and simplify the product tex 8 5i 2 tex Select the product A 39 B 89 C tex 39 80i tex D tex 89. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Multiply and simplify the product: [tex](8-5i)^2[/tex].

Select the product:

A. 39
B. 89
C. [tex]39-80i[/tex]
D. [tex]89-80i[/tex]

Answer :

To find the product [tex]\((8 - 5i)^2\)[/tex], we need to multiply the complex number by itself. Here’s a step-by-step method to simplify the expression:

1. Start with the expression [tex]\((8 - 5i)^2\)[/tex].

2. Apply the formula for squaring a binomial: [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex].
- Here, [tex]\(a = 8\)[/tex] and [tex]\(b = 5i\)[/tex].

3. Calculate each part:
- [tex]\(a^2 = 8^2 = 64\)[/tex].
- The term [tex]\(-2ab = -2(8)(5i) = -80i\)[/tex].
- For [tex]\(b^2\)[/tex], calculate [tex]\((5i)^2 = (5^2)(i^2) = 25(-1) = -25\)[/tex] since [tex]\(i^2 = -1\)[/tex].

4. Add the results together:
- Combine the real parts: [tex]\(64 + (-25) = 39\)[/tex].
- The imaginary part remains [tex]\(-80i\)[/tex].

5. Write the simplified result:
[tex]\((8 - 5i)^2 = 39 - 80i\)[/tex].

Thus, the simplified product is [tex]\(39 - 80i\)[/tex].

So, the correct selection from the options provided is [tex]\(39 - 80i\)[/tex].

Thanks for taking the time to read Multiply and simplify the product tex 8 5i 2 tex Select the product A 39 B 89 C tex 39 80i tex D tex 89. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada