Questions on Algebra: Complex Numbers answered by real tutors!

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Question 1028454: Using logarithmic differentiation, find the derivative of F(x) = (x^2+5)^(cot2x). Write the derivative in terms of x.
Click here to see answer by stanbon(75887)

Question 1028454: Using logarithmic differentiation, find the derivative of F(x) = (x^2+5)^(cot2x). Write the derivative in terms of x.
Click here to see answer by robertb(5830)

Question 1029365: How can i transform in to Cartesian form? (or known as rectangular form)
The problem I'm having is, How can i find the Radian Value of and . Which is used to turn this polar form in to Cartesian form?
without Calculator!!
Thanks!!!!
Click here to see answer by Alan3354(69443)

Question 1029385: Find the values of x and y for which the complex numbers
(2x+3y)+i(2y-1) and 10+i(5-x) are equal.
Click here to see answer by ikleyn(52784)

Question 1029391: What is Subgroup
How To Find Subgroup
How To Verify It is subgroup or not
Click here to see answer by ikleyn(52784)

Question 1029407: How To Prove De Moivre Theorem
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Question 1029563: How do I simplify the expression -5+i/2i
Click here to see answer by stanbon(75887)

Question 1029663: If (1/2+1/2(i))^10 write in a+bi form
Click here to see answer by fractalier(6550)

Question 1029661: If (1/2+1/2(i))^10 write in a+bi form
Click here to see answer by fractalier(6550)

Question 1030349: Let d,e and g be real numbers and consider the function F(x) = (x-d)(x-e)(x-g). Using Calculus, find the x-coordinate of the point of the inflection for the given function.
Click here to see answer by mathmate(429)

Question 1030353: Use Calculus. For what value of a is the following equation true?
lim ((x+a)/(x-a))^x = e
x->inf
Click here to see answer by Edwin McCravy(20056)

Question 1030353: Use Calculus. For what value of a is the following equation true?
lim ((x+a)/(x-a))^x = e
x->inf
Click here to see answer by robertb(5830)

Question 1030340: Solve the equation. Write any complex solutions in standard form for a complex number. (Enter your answers as a comma-separated list.)
8x^3+4x^2-26x=0

Click here to see answer by ikleyn(52784)

Question 1030347: Using Newton's Method, find the fourth approximation x4 to the root of x^3-2x-5=0 starting with x1=5.
Click here to see answer by Fombitz(32388)

Question 1030357: Optimization
The power absorbed by a circuit is p(x) = ((V^2)x)/(R+x)^2 where R is the resistance in ohms and V is the voltage in volts. Find the value of x that maximizes the power absorbed.
Click here to see answer by Fombitz(32388)

Question 1030294: I don't understand what this means? Like I don't understand how to figure out if it's all even or all odd exponents.
Make a generalization about the exponents of imaginary numbers, regarding whether or not all even or all odd exponents result in real or imaginary numbers. Explain and prove your statement with actual examples and at least one complete sentence that supports your generalization
Click here to see answer by ikleyn(52784)

Question 1031104: Calculus Problem.
Prove that F(x) = 4x^3+x has no relative max or min without graphing.
Click here to see answer by stanbon(75887)

Question 1030677: Find the roots of (-1+sqrt 3i)^3/2 leaving the answer in polar from.
Thanks
Click here to see answer by stanbon(75887)

Question 1031107: Consider the function f''(x) = cosx+sinx with f'(x) = 5 and f(0) = 2. What is f(x)?
Click here to see answer by Alan3354(69443)

Question 1031106: What is the antiderivative of g'(x) = e^x+15(1+x^2)^-1
Click here to see answer by ewatrrr(24785)

Question 1030863: 1 galons = 128 ounces
1 liter = 33.8 ounces
1 quart = 32 ounces
1 pint = 16 ounces
According to the tables below , which one of the following contain the most liquid container is full?
A) 2.5 liter bottle
B) 3/4 gallon jug
C) 5.5 pint carton
D) 3.5 quart vase
Click here to see answer by LinnW(1048)

Question 1031153: The following equation has denominators that contain variables. for this equation write the value or values of the variable that make a denominator zero. these are the restrictions on the variable. keeping the restrictions in mind, solve the equation.
2/11x + 1/4 = 81/22x - 1/3
My work for solving the equation is (2/11)x + 1/4 = (81/22)x - 1/3
24 x + 33 = 486 x - 44
77 = 462 x
x = 77/462
x = 7/42
x = 1/6
Click here to see answer by josgarithmetic(39617)

Question 1031245: Assume that f''(x) = cosx + sinx with f'(x) = 5 and f(0) = 2. What is f(x)?
Click here to see answer by ikleyn(52784)

Question 1031241: Use L'Hospital's Rule to find the limit of (1+2x)^(4/x) as x approaches 0.

Click here to see answer by solver91311(24713)

Question 1031289: Please help me solve the following equation.
(3-2x)�(sqrt ( 2x )-3)= (sqrt (2x)-2)
Click here to see answer by Alan3354(69443)

Question 1031398: How do you solve the inequality x^2+6x <= -8
Click here to see answer by solver91311(24713)

Question 1031467: What are two complex numbers with a product of 10. Can you show them in formula please?
Click here to see answer by Fombitz(32388)

Question 1031467: What are two complex numbers with a product of 10. Can you show them in formula please?
Click here to see answer by Edwin McCravy(20056)

Question 1032054: What are all the complex fourth roots of -81?
Click here to see answer by Alan3354(69443)

Question 1032217: What is the sum of: (14-5i)+(-8+12i)
Thanks much.
Click here to see answer by Alan3354(69443)

Question 1032244: 1. Use what you have learned to find the solutions of the polynomial equation shown below.
x4 + 5x3 ‒ x2 ‒ 50x ‒ 90 = 0 if x2 ‒ 10 is one of the factors.
Be sure to discuss real and complex solutions and how these solutions will affect the graph of the polynomial equation.

2. Use what you have learned in this lesson to determine all of the values for k that would give complex solutions to the equation shown below.
3x2 ‒ 8x + k = 0
Describe how you know your values for k give complex solutions to the equation.
Then, write a quadratic equation using a value of k that will have complex solutions and solve.

(Note: Please show your work so that I can understand your logic. Thank you.)
Click here to see answer by josgarithmetic(39617)

Question 1032245: 1. A polynomial function is shown below.

f(x)=x^6 + 12x^5 + 43x^4 + 22x^3 - 138x^2 - 280x - 200

a. Find the real zeros of f (x).
b. Express f (x) in terms of linear factors.
c. Find all of the zeros of f (x).

Click here to see answer by robertb(5830)

Question 1032243: 1. Create different sets of expressions that satisfy each desired outcome:
a. Find a pair of complex binomials whose sum is 8 + 9i.
b. Find a pair of complex binomials whose difference is -2 + 6i.

2. Make a generalization about the exponents of imaginary numbers, regarding whether or not all even or all odd exponents result in real or imaginary numbers. Explain and prove your statement with actual examples and at least one complete sentence that supports your generalization.

(Note: Please show all work so that I can understand your logic. Thank you)
Click here to see answer by KMST(5328)

Question 1032246: 1. Create two different rational polynomial expressions with the following constraints:
�one expression is undefined when x = 4,
�the other is undefined when x = ‒2 or 0.
Then, rewrite both as equivalent expressions, with a common denominator.

2. The expression G over H is multiplied with another rational expression, and the product is 2. What is the other rational expression?
(Note: Please show all work so that I can understand your logic. Thank you.)
Click here to see answer by KMST(5328)

Question 1032247: 1. Use the focus-directrix definition of a parabola to answer the following questions.
1) How would the shape of the parabola change if the focus were moved up, away from the directrix? How would we describe p?
2) How would the shape of the parabola change if the focus were moved down, toward the directrix? How would we describe p?
3) How would the shape of the parabola change if the focus were moved down, below the directrix?

2. Given:
y = 3x^2
1) Write the equation of a parabola that contains the point (2, ‒12) that is congruent to the parabola that is given. Describe the series of transformations that would move the given parabola to your parabola.
2) Write the equation of a parabola that contains the point (0, 8) that is congruent to the parabola that is given. Describe the series of transformations that would move the given parabola to your parabola.
3) Write the equation of a parabola that is similar (not congruent) to the given parabola that does NOT contain the point (0, 0), but does contain the point (2, 2).

Note: Please show all work so that I can understand how to do the problem. Thank you.

Click here to see answer by KMST(5328)

Question 1032805: Find the derivatives of the following functions
(a) f(x) = sqrt x cos x ( sqrt is only on x )
(b) g(x) = (x^3 + 1)/sin x
(c) h(x) = e^x sin(2x) (d) k(x) = x^2 / log x
Click here to see answer by ewatrrr(24785)

Question 1032865: If (5x−2)^2=ax^2−bx+c, what is the value of a+c^2?
Click here to see answer by stanbon(75887)

Question 1032864: If (3x+5)^2=ax^2+bx+c, what is the value of a+b+c?
Click here to see answer by josgarithmetic(39617)

Question 1032864: If (3x+5)^2=ax^2+bx+c, what is the value of a+b+c?
Click here to see answer by ikleyn(52784)

Question 1032873: C={1, 4, 9, 16,...}
C is a set of x, where x depends on n. x =
Click here to see answer by ikleyn(52784)

Question 1033399: find the smallest integer a > 2 such that 2/a, 3/a+1, 4/a+2, 5/a+3, 6/a+4 its very urgent plzz help me this question is from number theory

Click here to see answer by Alan3354(69443)

Question 1033758: Good day,
Kindly assist. What is the sum of twenty and twenty-five?
Click here to see answer by ikleyn(52784)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380