# Complex numbers Questions and Answers

Algebra
Complex numbers
The 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 numbers
American 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 numbers
You 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 numbers
Without 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 numbers
The reference angle of433° is The reference angle of -257° is The reference angle of 208° is
Algebra
Complex numbers
For 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 numbers
Factor 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 numbers
Kevin 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 numbers
Write in radical form. Do not simplify. 14x¹/⁴ = ________
Algebra
Complex numbers
Asume 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 numbers
Find 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 numbers
The 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 numbers
Use 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 numbers
Identify 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 numbers
If a function has a horizontal asymptote, it cannot have a vertical asymptote. a) False b) True
Algebra
Complex numbers
A 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 numbers
Complete 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 numbers
Determine 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 numbers
Sketch 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 numbers
The 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 numbers
Use 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 numbers
The 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 numbers
Write in the form a + bi, where a, b ∈ R. {(2 - i)(4 - 3i)²}/(3 + 2i)
Algebra
Complex numbers
Using 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 numbers
Find 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 numbers
For 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 numbers
8500 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 numbers
Which 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 numbers
Multiply. (7 +3i)(-4-3i) = (Simplify your answer. Type your answer in the form a + bi.)
Algebra
Complex numbers
1. 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 numbers
Find 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 numbers
The 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 numbers
The price of a video game system dropped by 18%. What is the current price if it used to be \$140?
Algebra
Complex numbers
Find the percent change to the nearest percent: 200 students to 456 students.
Algebra
Complex numbers
Prove 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 numbers
z2=8.6exp(3.245i) Convert z into Cartesian coordinate Pls use matlab to solve it and provide screenshots
Algebra
Complex numbers
Let 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 numbers
The 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 numbers
Write the expression in rectangular form, x + y i, and in exponential form, reiθ [√3(cos π/12 + i sin π/12)]^8
Algebra
Complex numbers
Find 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 numbers
Let Z[√3] = {a +b√√3 : a and b € Z}. Then prove that Z[√3] is a FD.
Algebra
Complex numbers
Solve 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 numbers
What is the maximum profit? \$126210.00 there is no maximum profit \$210.00 \$127170.00 \$230.00
Algebra
Complex numbers
How 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 numbers
A) 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 numbers
Find 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 numbers