Complex numbers Questions and Answers
Algebra
Complex numbersFind the quotient of the complex numbers. Leave your answer in polar form.
Z2
N
Z₁
21
22
*
2₁ = 6 (cos+ i sin ) 22=7 [cos + i sin
5
5
11
11
11

expression T
Algebra
Complex numbersWrite the number i √9 in simplest form, without a negative radicand.
i√9 =_________ (Simplify your answer. Type an integer or a fraction.)
Algebra
Complex numbersCalculate √43i. Give your answer in a + bi form. Give the solution with smallest positive angle.
Round to at least one decimal place.
Algebra
Complex numbersCalculate √2+4i. Give your answer in a + bi form. Give the solution with smallest positive angle.
Round to at least one decimal place.
Algebra
Complex numbersA group of friends is planning to go to Europe 3 years from now and have agreed to set aside $150 each month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 6% per year compounded monthly, how much money will be in their travel fund at the end of the third year?
Algebra
Complex numbersIn an orthonrmal cordinate system for thetriangle, a circle inscribed in a triangle with vertices 0 (0.0), P(a.0) and Q(0.a) has a radius of 1. What is the area of this triangle? answer is 3+2√2
Algebra
Complex numbersLet L. be the line with parametric equations
x = 9+31
y=43t
z=7
Find the vector equation for a line that passes through the point P (6, 9, 9) and intersects L at a point that is distance 4 from the point Q(9.4.7). Note that there are two possible correct answers. Use the square root symbol '√' where needed to give an exact value for your answer.
Algebra
Complex numbersThe area, A, in square feet, of the base of a rectangular storage bin in a warehouse is given by the function A(x) = 2x² + 36x, where x is the width, in feet, of the storage bin.
Part A: Which of the following statements would be TRUE?
The xintercepts of the function are 0 and 8, which are a lower bound and an upper bound for the possible values of the length of the storage bin.
The xintercepts of the function are 0 and 8, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
The xintercepts of the function are 0 and 18, which are a lower bound and an upper bound for the possible values of the length of the storage bin.
The xintercepts of the function are 0 and 18, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
Algebra
Complex numbersThe height, h, in feet of the tip of the minute hand of a wall clock as a function of time, t, in minutes can be modeled by the equation h=0.75cos(π/30*(t15))+8 Which number (from 1 to 12) is the minute hand pointing to at t=0?
3
6
9
12
Algebra
Complex numbersSolve the equation.
2y + 2(y8)= 4y 2(y10)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is
(Simplify your answer.)
B. The solution is all real numbers.
C. There is no solution.
Algebra
Complex numbersA football team scored 73 points during a game from touchdowns (6pts each), extra points (1pt
each), and field goals (3pts each).
The coach chastised the kicker afterward for only making half of their extra point attempts. The
assistant coach remarked that they made one less field goal than touch downs.
How many touchdowns, extra points, and field goals did they make?
The team made Number
and made Number field goals.
touchdowns but only made Number
extra point attempts,
Algebra
Complex numbersA ball is projected directly upward from an initial height of 200 feet with an initial velocity of 64 ft per second. The function s(t) = 16t² + 200t +64 describes the height of the ball in terms of time t. Find the maximum height that the ball reaches. (7 points)
Algebra
Complex numbers23. Suppose that point p is on a circle with
radius r = 15 cm, and ray op is rotating
with W = π rad / see.
a. Find the distance traveled by P along the
circle in time t = 12 sec.
b. Find the linear speed v of P.
Algebra
Complex numbersA rectangle with constant area has possible lengths and widths as shown in the table below.
Width vs. Length of a Rectangle
Width (w)
2
4
6
8
Which equation can be used to find any corresponding length and width that fit the pattern in this table?
0 1 =
Length (/)
37.5
18.75
12.5
9.375
where / is the length, w is the width, and k is a constant (w* 0)
O = mw+b, where / is the length, w is the width, and m and b are constants
O
W:
2, where / is the length, w is the width, and k is a constant
/= kw
/= aw², where / is the length, w is the width, and a is a constant
Algebra
Complex numbersThe voltage V of an audio speaker can be represented by V4/P, where P is the power of the speaker. An engineer wants to design a speaker with 484 watts of power. What will the voltage be?
volts
GITTIS
Algebra
Complex numbersIn this problem, p is in dollars and x is the number of units.
The demand function for a certain product is p = 121  x² and the supply function is p = x² + 6x + 41. Find the equilibrium point.
(L
(x, p) =
Find the consumer's surplus there. (Round your answer to the nearest cent.)
Algebra
Complex numbersFor the equation 6x + 5y = 30, (a) write it in slopeintercept form, (b) give the
slope of the line, (c) give the yintercept, and (d) graph the line.
...
(a) The slopeintercept form of the equation is
(Simply your answer. Use integers or fractions for any numbers in the equation.)
(b) The slope is
(Type an integer or a simplified fraction.)
(c) The yintercept is
(Type an ordered pair, using integers or fractions.)
(d) Use the graphing tool to graph the equation.
Click to
enlarge
graph
10
P
134
224435
10
75
COME
8
6
8
10
P
M
2201
NOTE
A
10
Algebra
Complex numbersReview the following words and rewrite
them below the inequality in which they
would apply. (Words could be used more
than once or not at all.)
Union And Or Intersection Compound
Inequality
3x1< 4
123x ≥ 5
Algebra
Complex numbersThe conjugate of a complex number a + bi is 25 + 3i. What is a + bi?
O25+ 3i
253i
Algebra
Complex numbersDetermine the domain and range of the given quadratic function below. Enter your answer using interval notation.
f(x) = 3x² + 12x  2
(a) Domain:
(b) Range:
Algebra
Complex numbers5 Solve your given pair of complex numbers placing them
on an Argand diagram.
B = 3 + 2j C = 3  2j
(a) X+Y
(b) YX
Algebra
Complex numbersIdentify the conic section represented by the equation by rotating axes
to place the conic in standard position.
Find an equation of the conic in the rotated coordinates, and find the
angle of rotation.
Choose one ▾
NOTE: Round your answer to one decimal place if needed.
0
7x² + 10xy + 7y² = 24
=
Algebra
Complex numbersThe price that a farmer receives for radishes is $62.00 per
cwt. (100 pounds). The price for processed radishes is
$75.00 per cwt and the price for processed radishes at the
retail level is $2.15 per pound. The conversion factor for
processed radishes is 1.175.
What is the farmtoretail price spread?
Algebra
Complex numbers5. y 3sin(12(x+π/24)) + 1
5. Write the equation of a sine curve, with smallest possible phase shift, if it has a maximum at
(4) and the nearest minimum to the right at (₁2).
Algebra
Complex numbersTo determine the distance between two
aircraft, a tracking station continuously
determines the distance to each aircraft
and the angle A between them (see figure).
Determine the distance a between the
planes when A= 38°, b = 39 miles, and c =
18 miles. (Round your answer to one
decimal place.) a =
Algebra
Complex numbersf(x) is a thirddegree polynomial having only real coefficients. It has 1 and 2i as zeros, and the yintercept(0, 3). Find f(x).
Algebra
Complex numbersLet : R³Prove thatdefinition!)πR2 be the projection function given by (x, y, z) = (x, y).is a continuous function. (Extra Credit if you use the ε8
Algebra
Complex numbersHow far away from a lighthouse on shore can a
ship be seen if the observer in the lighthouse is
100 ft above the surface of the Earth? Radius
of the Earth is 20.93 x 10^6 feet
1000 FT
5000 FT
22032 FT
10297 FT
Algebra
Complex numbersGeometry
Determine each of the following for the function
y= 6 cos(5(x +45)) – 3. Justify your answer.
i.The amplitude
ii.The period
Formula: 2TT/K=360/K (calculate exact
number)
iii.The phase shift
iv.The vertical shift of the function
b. Sketch the one cycle of the function in part (a)
on grid paper without using a table of values.
Explain your reasoning.