Questions on Algebra: Complex Numbers answered by real tutors!

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Question 1210389: The function f(x) = (1\x) is decreasing on its domain ( true or false)

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Question 1210389: The function f(x) = (1\x) is decreasing on its domain ( true or false)

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Question 1210389: The function f(x) = (1\x) is decreasing on its domain ( true or false)

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Question 1210388: The function f(x) = (1\x) is monotonic on its domain ( true or false) ?

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Question 1210380: Solve the equation [x² + 2x + 5] - [x + 1] = 6, where the symbol [ ] denotes the greatest integer function (floor function).

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Question 1210376: find the domain and range of f(x) = (x)/(sqrt(1 - ((sqrt(- x)))^2))
Click here to see answer by Edwin McCravy(20054)

Question 1210376: find the domain and range of f(x) = (x)/(sqrt(1 - ((sqrt(- x)))^2))
Click here to see answer by mccravyedwin(405)

Question 1210374: let x , y \[Element] R , prove that , 1) | x + y | = | x | + | y | \[DoubleLeftRightArrow] x . y \[GreaterEqual] 0, 2) | x - y | = | x | - | y | \[DoubleLeftRightArrow] (x - y) y \[GreaterEqual] 0, 3) | x - y | = | x | + | y | \[DoubleLeftRightArrow] x . y \[GreaterEqual] 0
Click here to see answer by ikleyn(52747)

Question 1210370: Using the discriminant method, find the range of the function:
y =(x+1)/(sqrt(x² - 5))
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Question 1210370: Using the discriminant method, find the range of the function:
y =(x+1)/(sqrt(x² - 5))
Click here to see answer by mccravyedwin(405)

Question 1210369: find the range of f(x) = 1/(sqrt(x + 1) + sqrt(x - 1))
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Question 1210367: find the range of :
١) f(x) = sqrt(4 - x ^2) + x
٢)f(x)= sqrt(x- 3)- sqrt(x- 2)
Click here to see answer by greenestamps(13195)

Question 1210367: find the range of :
١) f(x) = sqrt(4 - x ^2) + x
٢)f(x)= sqrt(x- 3)- sqrt(x- 2)
Click here to see answer by ikleyn(52747)

Question 1210364: Let z1 and z2 be two complex numbers such that |z1| = 5 and z1/z2 + z2/z1 = 0. Find |z1 - z2|^2.
Click here to see answer by ikleyn(52747)

Question 1210364: Let z1 and z2 be two complex numbers such that |z1| = 5 and z1/z2 + z2/z1 = 0. Find |z1 - z2|^2.
Click here to see answer by CPhill(1959)

Question 1210362: find the domain of f (x) = (7^(x - 3))^1/(x - 1)
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Question 1210362: find the domain of f (x) = (7^(x - 3))^1/(x - 1)
Click here to see answer by greenestamps(13195)

Question 1210356: find the range of
f(sqrt(x)) = x + 1
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Question 1210264: Find : limt((floor(x/3)-1)/(x-3)) , when (x→3)
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Question 1210265: find : limit (floor ((x)/3) - 1)/(x - 3) as x ---> 3
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Question 1210250: The number of ways to arrange 4 green balls, 3 red balls, and 2 white balls in a straight line such that no two balls of the same color are adjacent is equal to:
{79, 80, 81, 82}
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Question 1210249: In how many ways can 5 different cars be parked in a numbered circular parking lot such that two specific cars remain adjacent?
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Question 1167604: Consider
By finding the roots in cis form, and using appropriate substitutions,
Show:
=0
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Question 1167604: Consider
By finding the roots in cis form, and using appropriate substitutions,
Show:
=0
Click here to see answer by MathLover1(20849)

Question 1210151: How many ways can the letters of "lyltalqdr" be arranged such that no letter remains in its original position?
Click here to see answer by mccravyedwin(405)

Question 1210151: How many ways can the letters of "lyltalqdr" be arranged such that no letter remains in its original position?
Click here to see answer by CPhill(1959)

Question 1210151: How many ways can the letters of "lyltalqdr" be arranged such that no letter remains in its original position?
Click here to see answer by Edwin McCravy(20054)

Question 1167492: A polynomial P(x) has all real coefficients and z is a complex number.
If P(x)P(x') = 16, Find |P(x)|, giving reasons.
Note that x' is the conjugate of x and the answer should be 4.
I have no idea where to start with this question
Click here to see answer by ikleyn(52747)

Question 1169765: Claire needs to borrow $6000 to pay for NHL season tickets for her family. She borrows from the credit union with 36 monthly payments of $ each with an APR of %. What would Claire save in interest if she paid in full at the time of the payment and the credit union used the actuarial method for computing unearned interest?
Click here to see answer by ikleyn(52747)

Question 1170577: By solving another way, show that the exact value of is
I know that to solve this, the equation needs to be divided by specifically, but I don't know how to find the exact value.

Click here to see answer by CPhill(1959)

Question 1170557: Write and sketch: write the following complex numbers in rectangular form and sketch their representation in Argand diagram: 4 cis 120°
My rectangular form what i got: -2+(2sqrt3)i.
Is it correct and how do i SKetch it as a Argand diagram?
Click here to see answer by ikleyn(52747)

Question 1170558: Write and sketch: write the following complex numbers in rectangular form and sketch their representation in Argand diagram: 9 cis (3*pi/2) how do i sketch and get the rectangular form?
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Question 1209846: the expression 3/2+3i is equivalent to

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Question 1171501: The complex numbers z and w satisfy |z| = |w| = 1 and zw is not equal to -1.
(a) Prove that \overline{z} = {1}/{z} and \overline{w} = {1}/{w}.
(b) Prove that {z + w}/{zw + 1} is a real number.
Can you please explain in detail? I'm trying to grasp every aspect of the problem. Thanks
Click here to see answer by ikleyn(52747)

Question 1177560: 1) At what Chicago local time is the chicago-frankfurt flight due to arrive in Frankfurt.
2)If it is 11:45am in Adelaide, what time is it in Moscow?
3) If it is 11:20am in Caracas what time is it in Auckland?
HINT:
Leaving Departure Arrival City Time zone
Chicago 7:05pm* 2:45pm Chicago ST -6
Lisbon 7:35am 11.30am Frankfurt ST +1
Tokyo 12:30pm 8:45pm Shanghai ST +8
Auckland ST +11
Adelaide ST +8.5
*Previous Day ST: Summer Time
Click here to see answer by CPhill(1959)

Question 1209761: a) If 729^x = 3
and x^y = 216
find xy
b) If x - 5√x - 1 = 0
find x² + 1/x²

Click here to see answer by ikleyn(52747)

Question 1179802: Analyzing the functions below, compare and contrast the two functions in each problem situation. Be sure to use complete sentences in your comparison. Be sure to include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift between the two graphs.
1. y=3sin(2x) and y= 3cos(2x)

2. y=4sin(2x-π) and y=cos(3x- π over 2)
Click here to see answer by CPhill(1959)

Question 1181354: Prove that |z1 + z2 | < or = |z1|+|z2|. Use |z|^2 = mod z times z, Re(z) = (z + mod z)/ 2, and Re(z) < or = |z|. The inequality is known as the Triangle Inequality.
Click here to see answer by CPhill(1959)

Question 1182792: For n>_3, consider 2n points spaced regularly on a circle with alternate points black and white and a point placed at the centre of the circle.
The points are labelled -n,-n+1,...,n-1,n so that:
(a) the sum of the labels on each diameter through three of the points is a constant s, and
(b) the sum of the labels on each black-white-black triple of consecutive points on the circle is also s.
1.Show that the label on the central point is 0 and s=0. &
2.Show that such a labelling exists if and only if n is even.
Click here to see answer by CPhill(1959)

Question 1209595: limit x (1 - 2 cos ((pi x)/(3 x - sqrt3))) as x \[LongRightArrow] + \[Infinity]
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Question 1209633: Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|.

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Question 1209625: Express
\cfrac{1}{1 - \cfrac{1}{2 + \cfrac{1}{i}}}
in the form a+bi, where a and b are real numbers.
Click here to see answer by CPhill(1959)

Question 1209626: Find all complex numbers z satisfying the equation
\frac{z + 1}{z - 1} = 2 + i + \frac{-7 + 3z}{z}.
Click here to see answer by CPhill(1959)

Question 1209631: Find all complex solutions to the equation z^3 = 8i - (15 + 2i)z^2 + (7 - 4i)z.
Click here to see answer by CPhill(1959)

Question 1209632: What is the area of the region of the complex plane defined by |z| < 3 + 2|z - 1|?
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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