College Algebra Unit 4 - Milestone 4 with answers and rationale

College Algebra Unit 4 - Milestone 4 with answers and rationale 18 questions were answered correctly. 2 questions were answered incorrectly. 1 Angela is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. She uses the following formula to calculate voltage: The circuit she tests has a current of amps and a resistance of ohms. What is the voltage of the circuit? • • • • RATIONALE The voltage of the circuit is the product of the current and resistance. Recall that we can write as and as . Once we have expressed voltage in terms of , we need to multiply these two complex numbers by using FOIL. Multiply the first terms , the outside terms , the inside terms , and the last terms . Next, evaluate each multiplication. The expression multiplies to Next, combine like terms. and can combine to . Now we can simplify the last term, , which contains the imaginary unit squared. Recall that the is equivalent to , which can be substituted in our expression. . CONCEPT Complex Numbers in Electrical Engineering 2 Perform the multiplication and combine like terms. • • correct • • RATIONALE To multiply a set of three binomials, we can choose any two binomials to multiply using FOIL, and then distribute the remaining binomial to get a final product. Here, we will use FOIL to multiply , but you can choose any two binomials to start. Once the binomials have been multiplied together, evaluate the multiplication. . and combined is . can be expressed as . We still need to distribute the third binomial, . When multiplying these two terms, we will start The will need to be multiplied by everything inside the parentheses. times equals . This is one part of the final product. We will distribute into as well. When multiplying these two terms, we will start by distributing into . times equals . This is another part of the final product. The final step is to add these two parts together.