Final answer:
The product and simplified result of the multiplication (3 – 5i)(–2 + 4i) is 14 + 22i, corresponding to option b.
Step-by-step explanation:
The question asks to multiply and simplify the product of two complex numbers: (3 – 5i)(–2 + 4i). To do this, we use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first complex number by each term in the second complex number.
We have four multiplications to perform:
- (3)(-2) = -6
- (3)(4i) = 12i
- (-5i)(-2) = 10i
- (-5i)(4i) = -20i²
Remembering that i² = -1, we substitute -1 for i² in the product:
(-20)(-1) = 20
Now, we combine like terms (-6 and 20, 12i and 10i):
-6 + 20 + (12i + 10i) = 14 + 22i
Therefore, the product and simplified result is 14 + 22i, which corresponds to option b.