Questions on Algebra: Complex Numbers answered by real tutors!

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Question 1209238: "In how many ways can 7 students be divided into 3 unordered groups such that one group contains 1 student and the other two groups contain 3 students each?"

Click here to see answer by greenestamps(13195)

Question 1209246: We introduced i as a square root of -1. Does i + 1 itself have any square roots among the complex numbers? If so, name one. If not, answer with "None."
Click here to see answer by mccravyedwin(405)

Question 1209260: Find the equation of the tangents drawn from the point (4, 7) to the circle:
(x - 2)² + y² + 4y = 0.

Click here to see answer by mccravyedwin(405)

Question 1209260: Find the equation of the tangents drawn from the point (4, 7) to the circle:
(x - 2)² + y² + 4y = 0.

Click here to see answer by math_tutor2020(3816)

Question 1209260: Find the equation of the tangents drawn from the point (4, 7) to the circle:
(x - 2)² + y² + 4y = 0.

Click here to see answer by Edwin McCravy(20054)

Question 1209260: Find the equation of the tangents drawn from the point (4, 7) to the circle:
(x - 2)² + y² + 4y = 0.

Click here to see answer by AnlytcPhil(1806)

Question 1208370: 5 mathematics books, 5 physics books, and 5 chemistry books. In how many ways can they be arranged such that no two books of the same type are adjacent in the following cases:
1- In a straight line.
2- Around a circular table."
Click here to see answer by CPhill(1959)

Question 1207540: if f (x) + f ' (x) = 2 tan ^3(x) + tan ^2(x) + tan (x) + 1 , then f (x) = ...
Click here to see answer by CPhill(1959)

Question 1204865: if : f '(g (x)) = g '(x), f ''(x) \[Times] f '(x) = f (x), g '(3) = 2 g ''(3) = 2} then (d ^5 g)/(dx ^5 when x=3 is ... (9 , 10 ,18 , 24)
Click here to see answer by ElectricPavlov(122)

Question 1204864: if : f '(g (x)) = g '(x), f ''(x) \[Times] f '(x) = f (x), g '(3) = 2 g ''(3) = 2} then (d ^5 g)/(dx ^5)| = ... (9 , 10 ,18 , 24)
Click here to see answer by ElectricPavlov(122)

Question 1204107: We may define a complex conjugation operator K such that Kz =z^ * . Show that K is not a linear operator
Click here to see answer by ElectricPavlov(122)

Question 1203388: At Wazalendo SACCOS there is only one window for front office operations. The window is always opened from 7:00 am to 03:00 pm. It has been discovered that the average number of clients is 72 during the day and that the average service time is 5 minutes per person.
a) What is the average number of clients in the system?
b) Calculate the length of the queue.
c) What is the utilization factor of these SACCOS?
d) For how long will a customer be in this system?
e) Comment on the efficiency of this SACCOS in servicing its clients on the basis of calculations above.
Click here to see answer by asinus(45)

Question 1209286: All numbers (N) that are written in three decimal places, divisible by 11, and when divided by 11, the quotient equals the sum of the squares of its three digits.
Click here to see answer by math_tutor2020(3816)

Question 1209312: In the sequence 1, 3, 6, 10, 15, 21, ..., in the first 1000 terms of the sequence, how many terms are multiples of 5?
Click here to see answer by ikleyn(52747)

Question 1209312: In the sequence 1, 3, 6, 10, 15, 21, ..., in the first 1000 terms of the sequence, how many terms are multiples of 5?
Click here to see answer by greenestamps(13195)

Question 1194519: 1. Given: Z1= 2-2i , Z2= 3i and Z3= -3+i . Solve analytically and illustrate graphically. (Illustrate all 3 vectors and the result vector.)
(a) Z1-Z2+Z3 (b) Z3-Z2-Z1
Click here to see answer by proyaop(69)

Question 1194517: 1. Given: Z1= 2-2i , Z2= 3i and Z3= -3+i . Solve analytically and illustrate graphically. (Illustrate all 3 vectors and the result vector.)
(a) Z1-Z2+Z3 (b) Z3-Z2-Z1
2. Using the same given as Problem 1. Find:
(c) Z1*Z3 (d) Z3xZ2 (e) the acute angle between Z1 and Z2
Click here to see answer by proyaop(69)

Question 1209420: Select all the solutions to (x+2)2=−81

x=11

x=7

x=−11

x=−7

x=2+9i

x=−2+9i

x=2−9i

x=−2−9i

Click here to see answer by timofer(104)

Question 1209450: A triangle ABC, where |AB| = |AC|, a line CD is drawn from angle C and intersects side AB at D, such that |AD| = |CD| = |BC|. Find the measure of angle A in degrees.

Click here to see answer by CPhill(1959)

Question 1209455: find value of: cos(2π/7)+cos(4π/7)+cos(6π/7)
Click here to see answer by ikleyn(52747)

Question 1209455: find value of: cos(2π/7)+cos(4π/7)+cos(6π/7)
Click here to see answer by math_tutor2020(3816)

Question 1209502: Let be three positive numbers such that:
x^2 + y^2 + z^2 = 2(xy + xz + yz).
x + y + z + \frac{1}{xyz} > 4.

Click here to see answer by CPhill(1959)

Question 1209502: Let be three positive numbers such that:
x^2 + y^2 + z^2 = 2(xy + xz + yz).
x + y + z + \frac{1}{xyz} > 4.

Click here to see answer by ikleyn(52747)

Question 1209503: The function satisfies the following:
Find the rule of the fractional function that satisfies the following:
1. Its domain is ℝ / {2, -3}.

2. It has critical points at x = -2 and x = 1.

3. It has a local minimum at (-2, 1) and a local maximum at (1, 3). It is increasing on the interval ]-∞, -3[ ∪ [-2, 1] and decreasing on the remaining intervals of the domain.

4. It is concave upward on the interval ]-∞, -1] / {-3} ∪ ]2, +∞[.

5. It is concave downward on the interval [-1, 2[.

6. It has an inflection point at (-1, 2).

Click here to see answer by CPhill(1959)

Question 1209533: if a , b tow number \[Element] R , prove that :, |(a - b)/(sqrt(1 - a ^2) - sqrt(1 - b ^2))| < sqrt3
Click here to see answer by CPhill(1959)

Question 1209585: The number of ways to seat 3 students, 2 male teachers, and 4 female teachers around a round table with 10 chairs is how much?

Click here to see answer by Edwin McCravy(20054)

Question 1209585: The number of ways to seat 3 students, 2 male teachers, and 4 female teachers around a round table with 10 chairs is how much?

Click here to see answer by ikleyn(52747)

Question 1209599: The function D(x) = sin(|x|) is concave up on the interval
1. ]π, 2π[

2. ]-π, 0[

3. ]-4π, -3π[

4. ]-2π, -π[

Click here to see answer by Edwin McCravy(20054)

Question 1209599: The function D(x) = sin(|x|) is concave up on the interval
1. ]π, 2π[

2. ]-π, 0[

3. ]-4π, -3π[

4. ]-2π, -π[

Click here to see answer by mccravyedwin(405)

Question 1209599: The function D(x) = sin(|x|) is concave up on the interval
1. ]π, 2π[

2. ]-π, 0[

3. ]-4π, -3π[

4. ]-2π, -π[

Click here to see answer by ikleyn(52747)

Question 1209595: limit x (1 - 2 cos ((pi x)/(3 x - sqrt3))) as x \[LongRightArrow] + \[Infinity]
Click here to see answer by CPhill(1959)

Question 1185529: Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.
z = 27(3 + i), w = −9 − 9i
Click here to see answer by CPhill(1959)

Question 1185527: Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.
z = 27(3 + i), w = −9 − 9i
Click here to see answer by CPhill(1959)

Question 1185527: Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.
z = 27(3 + i), w = −9 − 9i
Click here to see answer by ikleyn(52747)

Question 1209622: Compute (-5 + 4i) + (-5 - 4i).

Express your answer in the form $a+bi$, where $a$ and $b$ are real numbers.
Click here to see answer by greenestamps(13195)

Question 1209624: Express (2 + i)(3 + i) in the form a + bi, where a and b a real numbers.
Click here to see answer by josgarithmetic(39613)

Question 1209629: Simplify (i + 1)(100) - (i - 1)(100).
Click here to see answer by ikleyn(52747)

Question 1209621: Compute (-5 + 3i) + (-5 - 3i).
Express your answer in the form $a+bi$, where $a$ and $b$ are real numbers.
Click here to see answer by ikleyn(52747)

Question 1209623: Compute
(2 + 3i) + (2 - 3i) + (-2 + 3i) + (-2 - 3i).
Click here to see answer by ikleyn(52747)

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