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Answer :
Let's multiply the complex numbers [tex]\((7 + 8i)\)[/tex] and [tex]\((6 - 5i)\)[/tex] to find the answer.
1. Distribute each part of the first complex number by each part of the second complex number:
[tex]\[
(7 + 8i)(6 - 5i) = 7 \cdot 6 + 7 \cdot (-5i) + 8i \cdot 6 + 8i \cdot (-5i)
\][/tex]
2. Calculate each term separately:
- [tex]\(7 \cdot 6 = 42\)[/tex]
- [tex]\(7 \cdot (-5i) = -35i\)[/tex]
- [tex]\(8i \cdot 6 = 48i\)[/tex]
- [tex]\(8i \cdot (-5i) = -40i^2\)[/tex]
3. Remember that [tex]\(i^2 = -1\)[/tex], so substitute [tex]\(-40i^2\)[/tex] with [tex]\(40\)[/tex] because [tex]\(-40 \times (-1) = 40\)[/tex].
4. Combine all real and imaginary parts:
[tex]\[
42 + 40 + (-35i + 48i) = 82 + 13i
\][/tex]
5. The final result is [tex]\(82 + 13i\)[/tex].
So, the answer is [tex]\( \boxed{82 + 13i} \)[/tex].
1. Distribute each part of the first complex number by each part of the second complex number:
[tex]\[
(7 + 8i)(6 - 5i) = 7 \cdot 6 + 7 \cdot (-5i) + 8i \cdot 6 + 8i \cdot (-5i)
\][/tex]
2. Calculate each term separately:
- [tex]\(7 \cdot 6 = 42\)[/tex]
- [tex]\(7 \cdot (-5i) = -35i\)[/tex]
- [tex]\(8i \cdot 6 = 48i\)[/tex]
- [tex]\(8i \cdot (-5i) = -40i^2\)[/tex]
3. Remember that [tex]\(i^2 = -1\)[/tex], so substitute [tex]\(-40i^2\)[/tex] with [tex]\(40\)[/tex] because [tex]\(-40 \times (-1) = 40\)[/tex].
4. Combine all real and imaginary parts:
[tex]\[
42 + 40 + (-35i + 48i) = 82 + 13i
\][/tex]
5. The final result is [tex]\(82 + 13i\)[/tex].
So, the answer is [tex]\( \boxed{82 + 13i} \)[/tex].
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