Final answer:
The simplified form of the complex number expression (8+10i)(5-8i) is 120 - 14i, by using the FOIL method to distribute and combine like terms.
Step-by-step explanation:
To simplify the expression (8+10i)(5-8i), we need to apply the distributive property, also known as the FOIL method in this context, which stands for First, Outer, Inner, Last. Here's how you expand the expression step by step:
- Multiply the first terms: 8 * 5 = 40
- Multiply the outer terms: 8 * (-8i) = -64i
- Multiply the inner terms: 10i * 5 = 50i
- Multiply the last terms: 10i * (-8i) = -80i². Since i² = -1, this becomes -80 * (-1) = 80
Now, combine like terms:
40 - 64i + 50i + 80 = 40 + 80 - 64i + 50i = 120 - 14i. Hence, the simplified form of (8+10i)(5-8i) is 120 - 14i.
Remember, when simplifying complex numbers, real parts are combined with real parts, and imaginary parts are combined with imaginary parts.