# Complex numbers Questions and Answers

Algebra

Complex numbersThe reference angle of 215 degrees is ______ degrees.
The reference angle of 320 degrees is _____ degrees.
The reference angle of -132 degrees is _____ degrees.

Algebra

Complex numbersAmerican General offers a 10-year annuity with a guaranteed rate of 4.95% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $1900 annually over the 10 year period?
How much should a customer pay for this annuity?

Algebra

Complex numbersYou need to build a trough for your farm that is in the shape of a trapezoidal prism. It needs to hold 100 liters of water. What are its dimensions (base 1, base 2, height, and depth)? You would also like to paint it, so you need to find its surface area. How much paint should you buy?

Algebra

Complex numbersWithout using a calculator, compute the sine, cosine, and tangent of 5π/3 by using the reference angle.
(Type sqrt(2) for √2 and sqrt(3) for √3.)
What is the reference angle?
In what quadrant is this angle?

Algebra

Complex numbersThe reference angle of433° is
The reference angle of -257° is
The reference angle of 208° is

Algebra

Complex numbersFor f(x) = a*sin(bx), use: Amplitude = |a|; Period T =2.π/|b| ;Section Width =T/4
Without graphing the function y = - 7 sin(9x), determine its amplitude, period, and section width (distance between critical points). Leave answers in exact form; type pi for π.
amplitude =?
period=?
section width=?

Algebra

Complex numbersFactor the following polynomial using the formula for the sum of two cubes.
z³+343
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. z³ + 343 = __________(Factor completely.)
B. The polynomial is prime.

Algebra

Complex numbersKevin and Randy Muise have a jar containing 67 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $12.95. How many of each type of coin do they have?
The jar contains ____ quarters.
The jar contains ____ nickels.

Algebra

Complex numbersAsume that the binary operation ab=a +6-540 is defined on 7 Which statement is
NOT correct?
is assosiative
is the identity element of (Z,*)
Every element of Z has an inverse
(25) dosed

Algebra

Complex numbersFind z, z₂, and z1//z2if z₁ = 6( cos 100+ i sin 100) and z₂ = 10 (cos 280+ i sin 280"). Write your answers in standard polar form with the argument in degrees.

Algebra

Complex numbersThe average weight of a male child's brain is 970 grams at age 1 and 1270 grams at age 3.
(a) Assuming that the relationship between brain weight y grams and age t years is linear, write a linear model for the data?
(b) What is the slope?
What does it tell you about brain weight?
The weight of a male human brain is decreasing by m grams/year.
A human male's brain reaches a maximum weight at age 3.
At birth, a human brain weighs 970 grams.
A human male's brain weight is constant for his entire lifespan.
The weight of a male human brain is increasing by m grams/year.
(c) Use your model to estimate the average brain weight at age 2.
(d) Use your school's library, the Internet, or some other reference source to find the actual average brain weight at age 2

Algebra

Complex numbersUse reference angles to find the exact value of the following expression. Do not use a calculator.
(CSC)5π/3
Determine the reference angle for 5π /3
The reference angle is _____. (Type your answer in radians. Use integers or fractions for any numbers in the expression. Type an exact answer needed.)

Algebra

Complex numbersIdentify the equation of the surface.
z=x²/4-y²/9
x²/4+y²/9+z²/4=1
z=x²/4+y²/9
x²/4+y²/9-z²/4=1
x²/4+y²/9=1

Algebra

Complex numbersIf a function has a horizontal asymptote, it cannot have a vertical asymptote.
a) False
b) True

Algebra

Complex numbersA new car is purchased for $47, 000 and over time its value depreciates by one half every 3.5 years. Write a function showing the value of the car after t years, where the annual decay rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of decay per year, to the nearest hundredth of a percent.
Function: f(t)=?
Growth ___% increase per year

Algebra

Complex numbersComplete the table of values for the following function and then plot the points to
graph the function by hand.
f(x)=1/2x²

Algebra

Complex numbersDetermine the intervals that make the following inequality true
x/3-(1/3x)<1/x
a) x>2
b) x<2
c) -2<x<0 and x>2
d) x<-2 and 0<x<2

Algebra

Complex numbersSketch graphs of each of the following:
(a) the polar equation r = 1 + 2sin(3θ)
(b) the curve determined by the parametric equations { x = t³/² + 1 }
{ y = √t }, t > 0

Algebra

Complex numbersThe function f(x) = x² +1/x³-4 has;
a) A Vertical Asymptote
b) A Horizontal Asymptote
c) An Oblique Asymptote
d) Both a and b
e) Both a and c
f) None of the above

Algebra

Complex numbersUse reference angles to find the exact value of the following expression. sin(-(π/4))
Determine the reference angle for-(π/4).
The reference angle is_____.(Type your answer in radians. Use integers or fractions for any numbers in the express)

Algebra

Complex numbersThe accompanying table shows the value of a car over time that was purchased for 18200 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the value of the car, to the nearest cent, after 16 years.
Years (x) Value in Dollars (y)
0 18200
1 14824
2 13651
3 11593
4 10590
Regression equation = ________

Algebra

Complex numbersUsing Euler's equation {e^i(x+y) = e^(ix) * e^(iy)
prove (1) sin x + sin y = 2sin{(x + y)/2} * cos{(x - y)/2}
(2) sin x cos y = {sin(x + y) + sin( x - y)} / 2
(3) cos x cos y = {cos(x + y) - cos(x - y)} / 2

Algebra

Complex numbersFind all of the solutions of 2 sin²(x) - 3 sin(x) - 2 = 0 between - π and π
a) x = π/6 and 5π/6
b) x = π/6 and -5π/6
c) x =-π/6 and 5π/6
d) x =− π/6 and – 5π/6

Algebra

Complex numbersFor the curve f(x) = -2(3)ˣ +3, the range of the function is:
a) R: {yly <3, y ≤ R}
b) R: {yly> 3, y ≤ R}
c) R: {yly ≤ 3, y ≤ R}
d) R: {yly> 3, y ≤ R}

Algebra

Complex numbers8500 dollars is placed in an account with an annual nearest year, how long will it take for the account interest rate of 7%. To the 59700 value to reach dollars?

Algebra

Complex numbersWhich quadrant would an angle of 14π/3 rads have its terminal arm, if rotated from standard position?
a) Quadrant III
b) Quadrant IV
c) Quadrant II
d) Quadrant I

Algebra

Complex numbersMultiply. (7 +3i)(-4-3i) =
(Simplify your answer. Type your answer in the form a + bi.)

Algebra

Complex numbers1. Factor the polynomial f(x)=x^4 +2x^3-2x^2 -6x -3 into factors of the form(x-c).
(b). Find any x-intercepts of the function y =f(x).
(c). Use a graphing calculator to sketch f(x) =x 4 + 2x 3 - 2x 2 - 6x - 3. Determine the
coordinates of the minimum value of f(x).

Algebra

Complex numbersFind the angle between v and w.
v = -2i+ 5j, w = 3i+9j
The angle between v and w is ____º.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Plot the complex number. Then write the complex number in polar form. Express the argument in degrees.
-11-11i
Plot the complex number on the complex plane to the right.
Write the complex number z=-11-11i in polar form. Select the correct choice below and fill in the answer box(es) within your choice.
(Type an exact answer, using radicals as needed.)

Algebra

Complex numbersThe maximum height of water near a tidal power station in New Brunswick is 6.4 metres at 4:30 am and the minimum height is 3.6 m, 6.2 hours later. What is the depth of the water at 6:45 pm?
a) 5.8 m
b) 5.6 m
c) 6.8 m
d) 2.8 m

Algebra

Complex numbersThe price of a video game system dropped by 18%. What is the current price if it used to be $140?

Algebra

Complex numbersProve that, for every positive integer n, there exist two regular polygons with the property that the ratio of the measure of an interior angle of one of the polygons to the measure of an interior angle of the other equals n+1/n

Algebra

Complex numbersz2=8.6exp(3.245i)
Convert z into Cartesian coordinate Pls use matlab to solve it and provide
screenshots

Algebra

Complex numbersLet A € Cnxn be a matrix with the spectrum A(A) = {a, b, c, d, e} (if you prefer a concrete example let A(A) = {1,3+i, 3-i, 1/2+2i, 1/2-2i}). Each eigenvalue occurs with an algebraic multiplicity of roughly n/5.
Explain why in general we can expect GMRES to converge in 5 steps.

Algebra

Complex numbersThe cities of Abnarca and Bonipto have populations that are growing exponentially. In 1980, Abnarca had a population of 26,000 people. In 1990, its population was 31,000. Bonipto had a population of 34,000 in 1980. The population of Bonipto doubles every 55 years. (Round your answers to the nearest whole number.)
(a) How long does it take the population of Abnarca to double?
(b) How long will it take for Abnarca's population to equal that of Bonipto?

Algebra

Complex numbersWrite the expression in rectangular form, x + y i, and in exponential form, reiθ
[√3(cos π/12 + i sin π/12)]^8

Algebra

Complex numbersFind the indicated roots of the following. Express your answer in the form found using Euler's Formula, Iz|neino
The cube roots of 64 (cos (3π/2) + isin ( 3π/2 ))

Algebra

Complex numbersSolve the system of equations by using any method. Write the solution as an ordered pair.
5x - 2y=19
7x - 3y= 27
Do not enter any spaces in the answer.
The solution is__

Algebra

Complex numbersWhat is the maximum profit?
$126210.00
there is no maximum profit
$210.00
$127170.00
$230.00

Algebra

Complex numbersHow much of the substance will remain after 10 years? Round to the nearest whole gram.
18 grams
184 grams
1 gram
490 grams
285 grams

Algebra

Complex numbersA) Find the polar form of the complex number z=5-3i.
B) Use the polar form above and DeMoivre's Theorem to find (5-3i)^6.

Algebra

Complex numbersFind the greatest common divisors of the following set of integers and find r.s and t
(such that the equation on the right is satisfied).
2+2+3+3
(c) c = 30,b= 75, a = 250, gcd(a, b, c) = 250r +75s + 30t
(d) c= 51, b = 27, a = 6, gcd(a, b, c) = 6r+27s+ 51t

Algebra

Complex numbersFind all the complex roots. Write the answer in exponential form.
The complex cube roots of 17 + 17 i.
Zo =
(Simplify your answer. Type an exact answer, using as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2л. Use integers or fractions for any numbers in the expression.)
Z₁ =
(Simplify your answer. Type an exact answer, using as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2π. Use integers or fractions for any numbers in the expression.)
2₂=
(Simplify your answer. Type an exact answer, using as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2л. Use integers or fractions for any numbers in the expression.)

Algebra

Complex numbersNote: Triangle may not be drawn to scale.
Suppose a = 5 and b = 6.
Find:
C
A
degrees
degrees
Give all answers to at least one decimal place. Give angles in degrees

Algebra

Complex numbersEvaluate the line Integral ∫(x² + y²) ds where "C" is The line segment from (-1, -1) To (2; 2).

Algebra

Complex numbersPerform the indicated operation and record answer in rectangle form
4 (cos 200° + i sin 200°)/2(cos 100° +isin 100°)