Answer :

Let's multiply and simplify the expression [tex]\((8 - 5i)^2\)[/tex].

1. To square a complex number of the form [tex]\((a - bi)\)[/tex], we'll use the formula:
[tex]\[
(a - bi)^2 = a^2 - 2abi + (bi)^2
\][/tex]

2. Plug in the values [tex]\(a = 8\)[/tex] and [tex]\(b = 5\)[/tex]:
[tex]\[
(8 - 5i)^2 = 8^2 - 2 \times 8 \times 5i + (5i)^2
\][/tex]

3. Calculate each part:
- [tex]\(8^2 = 64\)[/tex]
- [tex]\(-2 \times 8 \times 5 = -80\)[/tex] (so, [tex]\(-80i\)[/tex])
- [tex]\((5i)^2 = 25i^2\)[/tex]

4. Remember that [tex]\(i^2 = -1\)[/tex], so:
[tex]\[
25i^2 = 25 \times (-1) = -25
\][/tex]

5. Substituting these back in, we have:
[tex]\[
64 - 80i - 25
\][/tex]

6. Combine the real parts:
[tex]\[
64 - 25 = 39
\][/tex]

7. So, the expression simplifies to:
[tex]\[
39 - 80i
\][/tex]

Therefore, the simplified product is [tex]\(39 - 80i\)[/tex]. The correct option 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 39 80i D 89 80i. 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