University of Maryland College Park Complex Numbers Quiz

Show all the work! ……………………………………………………………….

Quiz 4
Show all the work!
1)   Find all real solutions of 2𝒙𝟒 + 𝒙𝟐 = 𝟑.
2)   Given the complex numbers 𝒛 = −𝟓 + 𝒊 and 𝒘 = −𝟒 + 𝟐𝒊, Find and
𝒛 𝒘
simplify , , 𝒛 ∗ 𝒘.
𝒘 𝒛
3)   Solve the inequality 𝟗𝒙𝟐 + 𝟏𝟔 ≥ 𝟐𝟒𝒙.
4)   Skippy wishes to plant a vegetable garden along one side of his house. In
his garage, he found 32 linear feet of fencing. Since one side of the
garden will border the house, Skippy doesn’t need fencing along that
side. What are the dimensions of the garden which will maximize the
area of the garden? What is the maximum area of the garden?
5)   The cost, in cents, to produce x cups of Mountain Thunder Lemonade
at Junior’s Lemonade Stand is 𝑪(𝒙)   =  𝟏𝟖𝒙   +  𝟐𝟒𝟎, 𝒙   ≥  𝟎 and the
price-demand function, in cents per cup, is
𝒑(𝒙)   =
 𝟗𝟎  -­‐‑  𝟑𝒙, 𝟎   ≤  𝒙   ≤  𝟑𝟎. Find the maximum profit.