# Complex numbers Questions and Answers

Algebra

Complex numbersLet L1 be the line passing through the point
P1=(-10, 5, 11) with direction vector →d1=
[−2, 3, 2]T, and let L2 be the line passing
through the point P2=(-34, 13, -3) with
direction vector →d2=[2, -5, 0]T. Find the
shortest distance d between these two
lines, and find a point Q1 on L1 and a point
Q2 on L2 so that d(Q1,Q2) = d. Use the
square root symbol 'V' where needed to
give an exact value for your answer.
d=
Q1=
Q2=
d = 4√33
Q₁=(-4,-4, 5)
Q2 = (-24, -12, -3)
Above is the answer, however, I am not
sure how to get to these solutions.

Algebra

Complex numbersFinancial Markets. The tock and bond markets are not the only
financial markets. Give two or three additional examples.

Algebra

Complex numbersWhich of the following explains why f(x) = log4x does not have a y-intercept? Check all that apply.
There is no power of 4 that is equal to 0.
There is no power of 4 that is equal to 1.
Its inverse does not have any x-intercepts.
Its inverse does not have any y-intercepts.

Algebra

Complex numbersSolve for x and check for extranepus roots.
(a) √x-1=1
x =
(b) √x - 2 = x - 2
X =
(c) √x + 6 = x
X =
(d) √3x + 16 = −8+√4x + 116
x =

Algebra

Complex numbers2. Show your work.
a. Simplify using i: -144
b. Find the absolute value: -1 + 3/
c. Simplify: (1-21)-(-2-i)
d. Simplify: (4- i)(2 + 5i)
e. Simplify:
-2-3i/6i

Algebra

Complex numbersNewton's Law of Cooling states that for a cooling substance with initial temperature To, the temperature T after t minutes can be modeled 0' by T = (To-T)e+T, where T is the surrounding temperature and r is the cooling rate of the substance. You remove a baked potato from a 400°F oven and place it on the counter in your 67°F kitchen. After 20 minutes, you measure the temperature of the potato to be 128°F. What will the temperature of the potato be after 26 minutes?
about 104°F
about 69°F
about 113°F
about 37°F

Algebra

Complex numbersWhat does the notation Ry-3x+1(DAB) mean?
Reflection
Rotation
Clockwise
Counter-clockwise
Around the origin to the axis
Over the x-axis
Over the y-axis
Over y-3x+1
180°
90°
270°

Algebra

Complex numbersDivide and express the result in standard form.
5i/2-7i
5i/2-7i
(Simplify your answer. Type your answer in the form a +bi. Use integers or fractions for any numbers in the expression.)

Algebra

Complex numbers.Find a general solution to
y" - 2y + 1y =12.5elt/t² + 1
Use a and b for the constants of integration associated with the homogeneous solution.
y =

Algebra

Complex numbersGiven the function h(x)=x²-7x³ +14x² -38x-60 has a zero of 1+3i, find the remaining zeros of the function (using algebra!). Write the function in factored form over the complex number system.
Zeros:__________________
Factored:______________

Algebra

Complex numbersEnter the expression or number that is required to solve the equation. Do not enter any blank spaces in your answers.
2(1 – 5x) = 72
a. Apply the distributive property: Write your response here...
b. When the constant term is moved to the right side, the resulting equation is:
c. Solve: X =
d. Solution set:

Algebra

Complex numbersThe property of equality states that we can add or the same number from each side of an equation and obtain an equivalent equation.
The property of equality states that we can or divide each side of an equation by the same nonzero number and obtain an equivalent equation.

Algebra

Complex numbersSolve the equation. Enter the solution set below. Recall that solution set notation is written in the form {p}, where P is the solution of the equation. (For example, if 2 is a solution, the solution set is {2}.)
-4 = 38 + 6x

Algebra

Complex numbersQuestion 36 (1 point) At a sandwich shop, 42% of customers buy a drink with their sandwich. Only 28% of customers buy a drink and chips with their sandwich. What is the probability that a customer who buys a drink also buys chips?
a)70%
b)about 66.7%
c)14%
d)1.5%

Algebra

Complex numbersAndy and Cheyenne are planning to have their wedding and reception at a local venue. The venue charges a rental fee of $2030.
The menu they have selected costs $36.75 per person.
a. If they have $7,500 saved for their reception, what is the maximum number of guests that can attend the reception without going over budget?
b. If, in addition to the meal, the couple wants to provide a beer and wine selection at the reception, there is an additional charge of $19.50 per person. In this case, what is the maximum number of guests that can attend the reception without going over budget?

Algebra

Complex numbersIf a linear equation is an identity, what is its solution set?
Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer.

Algebra

Complex numbersLet f(x) = - 3x + 7. Find each of the following:
f(a) =
2f(a) =
f(2a) =
f(a + 2) =
f(a) + f(2)=

Algebra

Complex numbersWrite the equation of the line in standard form.
slope = 3; (-1, 4)
Select one:
a. 3x=y-7
b. x-3y = -7
c. 3x-y = -7
d. y = 3x +7

Algebra

Complex numbersDarnell invested a total of $52,000 in two accounts. The first account earned 13% after one year.
However, the second account suffered a 5% loss in the same time. At the end of one year, the total
amount of money gained was $2,620.
LA
at 13%
at 5%

Algebra

Complex numbersSubtract and simplify.
(13+5i)-(4+3i)
(13+5i)-(4+3i) =
(Simplify your answer. Type your answer in the form a + bi.)

Algebra

Complex numbersDetermine whether each of the following mapping is a homomorphism (justify your
answer). If yes, find its kernel.
i. Define : Z → R by p(x) = x. (where Z and R are both groups under addition).
ii. Let(G,*) be a group under a binary operation and let y: GG be defined by
y(m) = m² for all meg.

Algebra

Complex numbersUsing Euler's equation (eixes) eix e¹g)
prove (1) sini+sing = 2 Sin (x+y). cos (x-4)
sin(x+y)+sin(x-y)
(2) Sinx cosy
(3) cost cosy = =
cos(x+y) - cos(x-y)

Algebra

Complex numbersSolve the following instance of SAT with the partial enumeration algorithm:
(Y₁ VY₂ VY₁) A (Y₁ V-Y₂) A(-Y₁ VY3) A(-Y₁ V-Y₁).

Algebra

Complex numbersIf a linear function has the points (-9,9) and (-1,8) on its graph, what is the rate of change of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice
A. The rate of change is
(Type an integer or a simplified fraction)
B. There is no solution

Algebra

Complex numbersFind the indicated roots. Express answers in trigonometric form. The sixth roots of 729( cos 0+ i sin 0). Choose the sixth roots of 729( cos 0 + i sin 0) below.

Algebra

Complex numbers11. (Equations with fractions/decimals) In college algebra, you will not only see equations with fractions, but you will also see equations with decimals. Keep in mind that decimals are just an alternative form for fractions.
a) Convert each decimal to a fraction:
b) Solve each equation.
0.7x + 2 = 1
x + 3 = 0.15x - 2

Algebra

Complex numbersWhich of the following values of x is not in the domain of g(x) = 4x-1/2x+1 ?
x=-1/12
(1) x = -1/2
(2) x =-1
(3) x=-1
(4) x = -3

Algebra

Complex numbersThe diagram shows a cable car following a straight path as it climbs up a mountain
slope from A to C. The cable car moves along AB for 500 m and then along BC for
another 400 m. The angle of elevation of B from A is 13⁰° and BD, the vertical height between B and C, is equal to 120 m.
2 marks
2 marks
2 marks
5 marks

Algebra

Complex numbersComplete the following simplification.
6 cis(47,000°)/cis(47,000°)= 6 cis_____

Algebra

Complex numbersSelect the correct answer below:
f(x)=2-log1/3 (2-1)
f(x)=1-log1/3 (x-1)
f(x)=2-log1/3 (2+1)
f(x)=1-log1/3 (x + 1)

Algebra

Complex numbers-6 + |x² + 2| <= 7y
8 + |x² + 3| <= 5y
Determine if (-3,3) is a solution to the system of inequalities above.
Select the correct answer below:
(A) Yes
(B) No

Algebra

Complex numbersAn investment of $76,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $5940. The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment.
(A) The first part of the investment was $____.
(B) The second part of the investment was $____.
(C) The third part of the investment was $____.

Algebra

Complex numbersFind f+g, f-g, fg and f/g
Determine the domain for each function.
f(x)=3x²-25x-18, g(x)=x-9
(f+g)(x) = (Simplify your answer.)

Algebra

Complex numbersChoose the correct statement.
For any angle 8, we have sin (-θ)=sin θ . (So sine is an odd function.)
For any angle 8, we have sin (-θ) = sin θ. (So sine is an even function.)
Neither of the above answers are true. (So sine is neither an odd nor an even function.)

Algebra

Complex numbersSolve the equation cotθ = √3 for all values of 0 in the domain 0 ≤θ < 27. Also, draw either a horizontal, vertical or diagonal line that goes through all solutions to the equation. Express your answer both in radians and degrees.

Algebra

Complex numbersFind the domain of the following function:
f(x)=1/ (x-8)(x - 6)
Select the correct answer below:
a) All real numbers
b) All real numbers except 8 and 6
c) All real numbers except - 8 and -6
d) All real numbers except 8 and -6
e) All real numbers except-8 and 6

Algebra

Complex numbersPlot the complex number. Then write the complex number in polar form
1-3i
Plot the complex number.

Algebra

Complex numbersFind zw. Leave your answer in polar form.
z = 3 (cos π/7 + i sin π/7)
w=5(cos π/11 + i sin π/11)

Algebra

Complex numbersIf f(z) has an inverse function f-¹(a), could either the graph of for the graph of f-¹ be symmetric with
respect to the y-axis? Please, explain your reasoning or use an example to illustrate your answer.

Algebra

Complex numbersHow long will it take for a $2500 investment to grow to $3500 at an annual rate of 7.5%, compounded quarterly? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth.
If necessary, refer to the list of financial formulas.

Algebra

Complex numbersc) An analyst models the spot interest rate with the following stochastic differential equation:
dR = (u - Rt)dt + dB, where u is a positive constant.
Using Ito's lemma on the function f(t, Rt) = exp(t) Rt show that:
R₁ = μ + exp(-t) (R₁ -μ) +exp(-(t-s)) dBs

Algebra

Complex numbersLet p be an odd prime number. Which integers a have the property that the inverse of a is congruent to a modulo p? Study the case p =7 and p = 11 first. Reorder the factors in (p-1)! in such a way that all pairs of inverses are written adjacent to one another. Compute (p-1)! modulo p after this reordering. What is (p-1)! mod p.