Final answer:
To multiply the complex numbers (4-5i) and (12+11i), distribute each term in the first complex number by each term in the second complex number, combine like terms, and apply i^2 = -1. The result in standard form is 103 - 16i.
Step-by-step explanation:
To perform the indicated operation and write the answer in standard form for the multiplication of two complex numbers, (4-5i) and (12+11i), we use the distributive property:
- (4-5i)(12+11i) = 4(12) + 4(11i) - 5i(12) - 5i(11i).
- This simplifies to 48 + 44i - 60i - 55i^2. Remember that i^2 = -1.
- Substituting i^2 with -1, we get 48 + 44i - 60i + 55.
- Combine like terms to obtain the standard form: 48 + 55 + (44i - 60i).
- Finally, the result is 103 - 16i.
The answer in standard form is 103 - 16i.