Questions on Algebra: Complex Numbers answered by real tutors!

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Question 1027375: Find all the roots of (sqrt -1), leave the answer in polar form.
Click here to see answer by greenestamps(13325)

Question 1027375: Find all the roots of (sqrt -1), leave the answer in polar form.
Click here to see answer by ikleyn(53742)

Question 652351: square root of -15 multiplied by square root of -3 divided by square root of 5
Click here to see answer by MathTherapy(10801)

Question 170747: I need some help with this problem.
i asked my friend to help me with a previous problem and he ended up just giving me the answer cause i still don't get it.
The one already answered ==
"":How i tried to work it out.
[]:my answer
1.
"2(x+6)(x-1)"
[x=6,(-1)]
Was that correct?
2.
?????
Please help me.

Click here to see answer by MathTherapy(10801)

Question 453794: solve by completing the square.
x^2+4x-12=0
Click here to see answer by ikleyn(53742)

Question 1165360: If Z1,Z2 are part of C such that Im(z1) = sqrt(3), |z2| = 2 and z1*z2 = 4(cos( 5pi/6 ) + sin( 5pi/6)i ). Find the values of Z1 and Z2.

Click here to see answer by CPhill(2189)

Question 1210495: Calculate the area of the triangle formed by the complex numbers , , and in the Argand plane, where is a complex number.
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Question 1165887: Express the roots of (-14+3i)^-2/5 complex number in polar form.
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Question 736989: 5-i / 4-3i
Click here to see answer by ikleyn(53742)

Question 742206: 4-i over
2-6i
can you walk me through the steps Im a little rusty.
This is what I got.
2 % i
7
Click here to see answer by ikleyn(53742)

Question 1210422: prove that : |{{ bc , c ^2, b ^2},{ c ^2, ca , a ^2},{ b ^2, a ^2, ab }}| = abc |{{ a , c , b },{ c , b , a },{ b , a , c }}|
Click here to see answer by ikleyn(53742)

Question 1210420: In how many ways can 5 people be seated in 8 chairs around a round table?
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Question 1210412: if limit e ^(x) sec (((b sin x))^2) = 0 as x \[LongRightArrow] - \[Infinity] , , then the possible values of b belong to the int erval ....
Click here to see answer by CPhill(2189)

Question 1184007: prove by mathematical induction:
1^5 + 2^5 + 3^5 + ... + n^5 = (1/12)n^2(n+1)^2(2n^2 + 2n -1)
Click here to see answer by ikleyn(53742)

Question 1210411: Prove by induction that for all n >= 1
1^ 5 +2^ 5 +3^ 5 +^ ...+ n ^ 5 = [n ^ 2 * (n + 1) ^ 2 * (2n ^ 2 + 2n - 1)] / 12 .
Click here to see answer by ikleyn(53742)

Question 1210398: Let f(x)= 1/(x+1). Determine the derivative of the -th iterate of , that is, compute , where denotes the composition of with itself times."
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Question 1210400: Let f(x)= 1/(x+1).
Determine the derivative of the -th iterate of , that is, compute , where denotes the composition of with itself times."
Click here to see answer by ikleyn(53742)

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

Click here to see answer by math_tutor2020(3835)

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

Click here to see answer by ikleyn(53742)

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

Click here to see answer by josgarithmetic(39790)

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

Click here to see answer by ikleyn(53742)

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

Click here to see answer by ikleyn(53742)

Question 1210376: find the domain and range of f(x) = (x)/(sqrt(1 - ((sqrt(- x)))^2))
Click here to see answer by Edwin McCravy(20077)

Question 1210376: find the domain and range of f(x) = (x)/(sqrt(1 - ((sqrt(- x)))^2))
Click here to see answer by mccravyedwin(419)

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(53742)

Question 1210370: Using the discriminant method, find the range of the function:
y =(x+1)/(sqrt(x² - 5))
Click here to see answer by ikleyn(53742)

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(419)

Question 1210369: find the range of f(x) = 1/(sqrt(x + 1) + sqrt(x - 1))
Click here to see answer by ikleyn(53742)

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(13325)

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(53742)

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(53742)

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(2189)

Question 1210362: find the domain of f (x) = (7^(x - 3))^1/(x - 1)
Click here to see answer by ikleyn(53742)

Question 1210362: find the domain of f (x) = (7^(x - 3))^1/(x - 1)
Click here to see answer by greenestamps(13325)

Question 1210356: find the range of
f(sqrt(x)) = x + 1
Click here to see answer by ikleyn(53742)

Question 1210264: Find : limt((floor(x/3)-1)/(x-3)) , when (x→3)
Click here to see answer by ikleyn(53742)

Question 1210265: find : limit (floor ((x)/3) - 1)/(x - 3) as x ---> 3
Click here to see answer by ikleyn(53742)

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}
Click here to see answer by ikleyn(53742)

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
Click here to see answer by ikleyn(53742)

Question 1167604: Consider
By finding the roots in cis form, and using appropriate substitutions,
Show:
=0
Click here to see answer by MathLover1(20855)

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(419)

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(2189)

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(20077)

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(53742)

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