# Complex numbers Questions and Answers

Algebra

Complex numbersWhich of the following statements is true?
(A) sin z / z2 has a removable singularity at z = 0.
(B) The function 1/zsinz2 has a pole of order 3 at z = 0.
(C) The function e2/z2 has a simple pole at z = 0.
(D) The function 1/z e^1/z has a removable singularity at = -0.
(E) For function f(z) = 1/z^3(1-z)^3, we have Reso f(z) = 0.

Algebra

Complex numbersGiven this table about Tuberculosis (TB), which is a disease that affects the lungs. Most Americans are tested for TB when they are young, and when they will be working with youth. What would the expression P(haveTB | Test positive) represent?
People Tested for TB
Have TB Does not have TB Total
Test Positive 198 98
Test Negative 2 9702 9704
total 9800
Select one:
a. Joint Relative Frequency
b. Marginal Relative Frequency
c Conditional Relative Frequency
d. None of these

Algebra

Complex numbers1. Below is a graph of the height of a passenger car on a Ferris wheel.
a. How does this function differ from other types of functions you have studied such as linear, polynomial, and exponential functions?
b. What is the domain of this Ferris wheel height function? What is the range?
2. Find a definition of periodic function and then rewrite it in your own words.
3. What other situations might be modeled by a periodic function?

Algebra

Complex numbersSolve for the exact solutions in the interval [0, 2π). If it has no solutions, respond with DNE.
8 sec² (x/2) = 4

Algebra

Complex numbersLet ø:G -> H be an isomorphism, show that
1.ø-¹: H->G is an isomorphism
2. if K≤ H, then ø-¹(K) ≤ G

Algebra

Complex numbersP(Z)= Z⁴ +(2-7i) Z⁸+ (-14-14i) z² + (-28+8i)Z+16i
please factorise the above equation.

Algebra

Complex numbersExpand log₃ (1/x²y3ᶻ) completely. Keep variables in the order that given in the original term. I.e. For log(), present the answer as log a-log 3-log b, but not log 3-log b + loga.

Algebra

Complex numbersA hockey coach wanted to know the relationship between the number of shots his team takes during a game and the
number of goals they score..
Shots 11 20 24 28 27 33 17 38
Goals 1 2 0 3 2 3 1 4
a) Write the linear regression function with values to the nearest TENTH.
b) Extrapolate how many shots would be required to score 5 goals. Round answer to nearest shot

Algebra

Complex numbersEvaluate J by means of Simpson's rule with n = 2m = 20 and h=0.05:
J = ¹∫₀e^(-x²)dx
Note that this integral cannot be evaluated by elementary calculus, but leads to the error function.

Algebra

Complex numbersStarting at point A, a ship sails 20 miles on a bearing of 200°, then turns and sails 40 miles on a bearing of 300°. Find the distance of the ship from point A.

Algebra

Complex numbersLet f(x) and g(r) be defined as follows:
f: (4,0)→ R. f(x) = ln(x-4)
9: R R. g(x)=x²-5
Calculate the following compositions and determine the range and domain of each of them.
Please note that drawing a graph of the composed function is not sufficient working to show
your answer for the domain and range.
(a) (fog)(x)
(b) (gof)(x)

Algebra

Complex numbersUse the graph below to answer the following questions. Be careful with the input and output variables. Not everything is x or y! What is the minimal degree that the function q could have? The zero at w = 1 would have multiplicity Write an equation using function notation, as in f(x), with the smallest possible degree for the function graphed above.

Algebra

Complex numbersFind the equation for the line that passes through the points (8, -5) and (-9, -1). Give answer in point-slope form. You do not need to simplify.
________

Algebra

Complex numbersComplete the following table. Remember that 180° = π radians.
Angle (degrees) 30⁰ 36° 45°
Angle (radians) π/6
Angle (radians)
Based on this, if x is an angle measurement in degrees, then the corresponding angle measure in radians is ___________ radians.

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 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 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 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?