Question

Select each statement below that is a correct step to simplify the problem completely. Complex answers should be in a+bi form.

(a) multiply by (3 - i)/(3 - i)
(b) the final answer is (1 + 3i)/10
(c) use FOIL to multiply the denominators
(d) distribute i to (3 - i)
(e) the final answer is (1/10) + (3i/10)

Answer 1

The correct steps to simplify the problem completely are: multiplying by (3 - i)/(3 - i), c) using FOIL to multiply the denominators, d) distributing i to (3 - i), eliminating terms wherever possible. Hence, c and d are correct.

Step-by-step explanation:

To simplify the problem completely, follow these steps:

1. Multiply by (3 - i)/(3 - i): This step helps in rationalizing the denominators and eliminates complex numbers in the numerator. For example, if you have the fraction (a + bi)/(c + di), multiplying it by (c - di)/(c - di) will eliminate the complex numbers.
2. Use FOIL to multiply the denominators: This step is used to multiply the two binomials in the denominator using the FOIL method (First, Outer, Inner, Last).
3. Distribute i to (3 - i): This step involves multiplying i to both terms in the parentheses.
4. Eliminate terms wherever possible: This step involves simplifying the algebra by combining like terms, canceling out common factors, and simplifying fractions.
5. Check the answer to see if it is reasonable: Finally, evaluate the simplified expression to ensure it is correct and makes sense in the context of the problem.