Unit Test — Cumulative exam Answers

Which property of multiplication is shown below? If x = 3 + 4i and y = 5 + 6i, x × y = y × x.

Consider the function represented in the table.

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

The following statements concern the modulus. Which statement is false?

The motion of a weight that hangs from a spring is represented by the equation . It models the weight’s height, h, in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 4 inches below the rest position? Round to the nearest hundredth, if necessary.

Consider the function f(x) = 10(x2 – 7x). What are the additive and multiplicative inverses?

A point of the form 25 +bi is 37 units from 13 – 31i. What is the value of b?

What is the quotient of ?

Consider z = 3 + 3i. What happens to the modulus and argument when z is raised to the 4th power?

Which statement is true about the graph of the equation ?

Given vectors u = ⟨3, 4⟩ and v = ⟨4, 3⟩, what is the measure of the angle between the vectors?

Review the diagram of the unit circle.

Which inequality is equivalent to ?

Review the proof of de Moivre’s theorem. Proof of de Moivre's Theorem [cos(θ) + i sin(θ)]k + 1A= [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1B= [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]C= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ) sin(θ)]D= cos(kθ + θ) + i sin(kθ + θ)E= cos[(k + 1)θ] + i sin[(k + 1)θ]

A waterwheel has a radius of 5 feet. The center of the wheel is 2 feet above the waterline. You notice a white mark at the top of the wheel. How many radians would the wheel have to rotate for the white mark to be 3 feet below the waterline?

Identify the horizontal and vertical asymptotes, if any, for the graph of f(x) shown. Check all that apply.

Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?

Which region on the unit circle contains a cube root of – 8 – 8i?