Final answer:
To simplify f(x)/g(x) with f(x) = 3 - i and g(x) = 2 + i, multiply by the conjugate of g(x), which is 2 - i, to find that the simplified form is 1 - i.
Step-by-step explanation:
To simplify the expression of f(x)/g(x) where f(x) = 3 - i and g(x) = 2 + i, we would multiply the numerator and the denominator by the conjugate of the denominator.
Step 1: Identify the conjugate of g(x), which is 2 - i.
Step 2: Multiply both the numerator and denominator by the conjugate of g(x):
- (f(x) * conjugate of g(x)) / (g(x) * conjugate of g(x))
- ((3 - i)(2 - i)) / ((2 + i)(2 - i))
Step 3: Perform the multiplication:
- Numerator: (3*2) + (3*(-i)) + (-i*2) + (i^2)
- Numerator: 6 - 3i - 2i - 1 (since i^2 = -1)
- Numerator simplifies to: 5 - 5i
Denominator: (2^2) - (i^2)
- Denominator: 4 - (-1)
- Denominator simplifies to: 5
Step 4: Simplify the expression:
(5 - 5i) / 5
Step 5: Divide each term in the numerator by the denominator:
1 -