Final answer:
To multiply the complex numbers (7-5i) and (-2-3i), apply the FOIL method to find product -29 - 11i.
Step-by-step explanation:
To multiply two complex numbers, (7-5i)(-2-3i), we use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Multiplying each part results in:
- First: 7 × (-2) = -14
- Outer: 7 × (-3i) = -21i
- Inner: (-5i) × (-2) = 10i
- Last: (-5i) × (-3i) = 15i²
Since i² = -1, we replace this in our equation:
-14 + (-21i + 10i) + 15(-1)
Combining like terms gives us:
-14 - 11i - 15
The final answer is:
-29 - 11i