Final answer:
To calculate the product of the complex numbers (2-4i), (3-2i), and (-5+3i), multiply them in pairs and simplify using the property that i² = -1 to get the result, which is 58 + 74i.
Step-by-step explanation:
The product of the complex numbers (2-4i), (3-2i), and (-5+3i) can be calculated by multiplying the numbers in pairs and then multiplying the result by the third number. First, we multiply (2-4i) by (3-2i), then we multiply the result by (-5+3i). Here's the step-by-step calculation:
- Multiply the first two complex numbers: (2-4i) * (3-2i) = 6 - 4i -12i + 8i². Since i² = -1, this simplifies to 6 - 16i - 8 = -2 - 16i.
- Now, multiply the result by the third complex number: (-2 - 16i) * (-5 + 3i) = 10 - 6i + 80i - 48i². Since i² = -1, this simplifies to 10 + 74i + 48 = 58 + 74i.
Therefore, the product of the complex numbers is 58 + 74i.