Answer :
To find [tex]\((8 - 5i)^2\)[/tex], we can use the formula for squaring a binomial, [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex].
1. Identify the values:
- [tex]\(a = 8\)[/tex]
- [tex]\(b = 5i\)[/tex]
2. Apply the formula for squaring a binomial:
[tex]\((8 - 5i)^2 = (8)^2 - 2(8)(5i) + (5i)^2\)[/tex].
3. Calculate each part:
- [tex]\((8)^2 = 64\)[/tex]
- [tex]\(-2(8)(5i) = -80i\)[/tex]
- [tex]\((5i)^2 = 25i^2\)[/tex]
4. Recall that [tex]\(i^2 = -1\)[/tex]. Therefore, [tex]\((5i)^2 = 25(-1) = -25\)[/tex].
5. Put it all together:
[tex]\(64 - 80i - 25\)[/tex].
6. Combine the real parts:
[tex]\(64 - 25 = 39\)[/tex].
7. The result is:
[tex]\(39 - 80i\)[/tex].
Thus, the product is [tex]\(39 - 80i\)[/tex].
1. Identify the values:
- [tex]\(a = 8\)[/tex]
- [tex]\(b = 5i\)[/tex]
2. Apply the formula for squaring a binomial:
[tex]\((8 - 5i)^2 = (8)^2 - 2(8)(5i) + (5i)^2\)[/tex].
3. Calculate each part:
- [tex]\((8)^2 = 64\)[/tex]
- [tex]\(-2(8)(5i) = -80i\)[/tex]
- [tex]\((5i)^2 = 25i^2\)[/tex]
4. Recall that [tex]\(i^2 = -1\)[/tex]. Therefore, [tex]\((5i)^2 = 25(-1) = -25\)[/tex].
5. Put it all together:
[tex]\(64 - 80i - 25\)[/tex].
6. Combine the real parts:
[tex]\(64 - 25 = 39\)[/tex].
7. The result is:
[tex]\(39 - 80i\)[/tex].
Thus, the product is [tex]\(39 - 80i\)[/tex].
