Questions on Algebra: Complex Numbers answered by real tutors!

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Question 1180194: is cos x = 0.25, find sin x
i have looked up tutorials but i am a bit confused.

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Question 1180194: is cos x = 0.25, find sin x
i have looked up tutorials but i am a bit confused.

Click here to see answer by MathTherapy(10549) About Me 

Question 1180262: Show all work. Be sure to answer both part A and B to the following questions.
Part A, Which of the following is a polynomial equation?
a.6x^2 + x + 2 = (6x-2)(x+4)
b.(5x-1)^2 = 25x^2 + 1
c.9(4a^2 - 4ab + b^2) = (6a - 3b)^2
d.(7x + 2)(x - y) = 7x(x - y) - 2y
Part B, Which expression is not equivalent to 16x^4 - y^4?
a.(2x-y)(2x+y)(4x^2 + y^2)
b.(2x)^4 - (y)^4
c.4x^2(4x^2 - y^2) + y^2(4x^2 - y^2)
d.(2x-y)(8x^3 + y^3)

Click here to see answer by MathLover1(20849) About Me 

Question 1180326: Prove, algebraically, that the following equations are polynomial identities. Show all of your work and explain each step. Use the Rubric as a reference for what is expected for each problem.
A. (2x+5)^2 = 4x(x+5) + 25
B. (4x + 6y)(x - 2y) = 2(2x^2 - xy - 6y^2)

Click here to see answer by josgarithmetic(39613) About Me 

Question 1180328: Find the number that is (1)/(3) of the way from 2(1)/(6) to 5(1)/(4)
Click here to see answer by ikleyn(52748) About Me 

Question 1180516: Find all solutions to the below equation, z  5  2i  3 , where z is a complex number,
and sketch the set of solutions on the complex plane.

Click here to see answer by Edwin McCravy(20054) About Me 

Question 1180527: Function 1: y=7sin(x+5)
Function 2:y=7cos(5x-1)
Part A: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 1.
Part B: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 2
Part C: write a sentence to compare and contrast the two functions

Click here to see answer by MathLover1(20849) About Me 

Question 1180524: Part A: For the function y=sin x , the value of 3pi over 2 is marked. At what point does this cycle end?
Part B: For the function y=cos x , the value of 2pi is marked. At what point did the cycle before this one begin?
Part C: Support your answers to Part A and Part B by showing all work.

Click here to see answer by ikleyn(52748) About Me 

Question 1180534: Find all solutions to the below equation, |z + 5 - 2i| =3 , where z is a complex number,
and sketch the set of solutions on the complex plane.

Click here to see answer by ikleyn(52748) About Me 
Question 1180534: Find all solutions to the below equation, |z + 5 - 2i| =3 , where z is a complex number,
and sketch the set of solutions on the complex plane.

Click here to see answer by Edwin McCravy(20054) About Me 

Question 1180663: Use De Moivre’s Theorem to solve for z and leave answer in polar form with the angle in radians

Z^4=-1+ j square root of 3

Click here to see answer by greenestamps(13195) About Me 

Question 1180661: Use De Moivre’s Theorem to solve for z and leave your answer in polar form with the angle in radians
Z^3 = -8

Click here to see answer by ikleyn(52748) About Me 

Question 1181073: If z is complex varibale and z' denote the conjugate of z.
Find the limit of (z')^2/z^2 where z approaches to zero?
[Note: Here ^ means power and / means division]

Click here to see answer by ikleyn(52748) About Me 

Question 1181018: Please help me solve this problem
Convert the General Equation 36y2-64x2-128x-144y-2512=0 to Standard form.
Sketch and determine the parts of the Hyperbola.
Parts of Hyperbola:
1. Center
2. Foci
3. Vertices
4. Length of Conjugate Axis B1, B2
5. End Points of Latus Rectum E1, E2, E3, E4
6. Asymptotes
7. Eccentricity
8. Length of LR
9. Length of Conjugate Axis
10. Length of Traverse Axis
Thank you and God bless

Click here to see answer by MathLover1(20849) About Me 

Question 1181165: Use De Moivre's Theorem to show that integral powers of (-1 + i)/(√2) are real, and which are imaginary
Click here to see answer by ikleyn(52748) About Me 

Question 1181339: Use De Moivre's Theorem to show which integral powers of +%28-1%2Bi%29+%2F+sqrt%28+2+%29+ are real, and which are imaginary.
Click here to see answer by ikleyn(52748) About Me 

Question 1181402: Use De Moivre’s Theorem to solve for z and leave the answer in polar form with the angle in radians
z^3 = −8

Click here to see answer by ikleyn(52748) About Me 

Question 1181459: z = 2 ( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } )
What will Z^4 be equal to

Click here to see answer by greenestamps(13195) About Me 

Question 1181458: Given 2i = ix (2−3i)−y (5+3i).What is the value of x and y:
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Question 1181499: solve ((z+1)^2) = 2(z^2), for z
Click here to see answer by ikleyn(52748) About Me 

Question 1181500: Prove that (z^n) + (z*)^n is always real for integer n
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Question 1181502: What are the roots of (z^2) - z(1 + i) + 5i = 0?
Click here to see answer by MathLover1(20849) About Me 
Question 1181502: What are the roots of (z^2) - z(1 + i) + 5i = 0?
Click here to see answer by ikleyn(52748) About Me 

Question 1181505: Given z = (1+i)/(√2), find (z)^(3/2)
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Question 1181503: What are the fifth roots of -32i?
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Question 1181497: If -2 is a root of ((z^3) - (8(z^2)) + (9z) + 58 = 0, what are the other two roots?
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Question 1181403: Given z1 = 2∠15°, ; z2 = 2∠150° and z3 = 3∠60°. Determine the following and leave the answers in rectangular form:
(z1)^2+z2 / z2+z3

Click here to see answer by greenestamps(13195) About Me 

Question 1181501: Check that (2 + i) is a root of (z^4) + (2(z^3)) - (9(z^2)) - 10z + 50 = 0. What are the remaining 3 roots?
Click here to see answer by ikleyn(52748) About Me 
Question 1181501: Check that (2 + i) is a root of (z^4) + (2(z^3)) - (9(z^2)) - 10z + 50 = 0. What are the remaining 3 roots?
Click here to see answer by greenestamps(13195) About Me 

Question 1181684: Find the fifth roots of -32i.
Click here to see answer by ikleyn(52748) About Me 

Question 1181681: Solve (z+1)^2 = 2z^2 for z.
Click here to see answer by Boreal(15235) About Me 

Question 1181683: Check that (2+i) is a root of +z%5E4+%2B+2z%5E3+-+9z%5E2+-+10z+%2B+50+=+0+. Find the remaining three roots.
Click here to see answer by ikleyn(52748) About Me 

Question 1181679: If -2 is a root of +z%5E3+-+8z%5E2+%2B+9z+%2B+58+=+0+, then find the other two roots.
Click here to see answer by ikleyn(52748) About Me 

Question 1182596: Factor the following expression completely given that one of the roots is 8:
w^3-8w^2-9w+72

Click here to see answer by mananth(16946) About Me 

Question 1182646: The 10 in term of an Ap is_27and in term is_12 what is the 18 in term?
Click here to see answer by greenestamps(13195) About Me 

Question 1182645: The 10 in term of an Ap is_27and in term is_12 what is the 18 in term?
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Question 1182669: Through what positive angle must a vector whose complex expression is -5 - 5i be rotated until it coincides in direction with the vector whose complex expression is 3 + 4i?

—-> Please help me on this problem, I get confused on how the angles can be rotated.

Click here to see answer by greenestamps(13195) About Me 

Question 1182854: X(1+2i)+y(3+5i)=-3
Click here to see answer by greenestamps(13195) About Me 

Question 1182970: Compute:
(1+√-2)/2-(1-√(-1/2))
There is a little note on the problem too:
"Since i%5E2=−1, then −1=±i. However, for this problem use the principal root of (−1), namely −1=i. For square root of a positive real number use principal root (the positive root) as well."

Click here to see answer by MathLover1(20849) About Me 

Question 1181369: Prove that |z1+z2| < or = |z1| + |z2|. Use |z|^2 = conjugate (z) times z, Re(z) = (z + conjugate (z)) / 2, and Re(z) < or = |z|. This inequality is known as the Triangle Inequality.
Click here to see answer by robertb(5830) About Me 

Question 1181682: Use De Moivre's Theorem to find an expression for cot3(theta).
Click here to see answer by robertb(5830) About Me 

Question 1183857: Each number is two times three less than the previous number. Starting with the number 0, build a sequence of 5 numbers
Click here to see answer by greenestamps(13195) About Me 
Question 1183857: Each number is two times three less than the previous number. Starting with the number 0, build a sequence of 5 numbers
Click here to see answer by ikleyn(52748) About Me 

Question 1183872: If x+y=5 and x and y are positive integers, what is the maximum possible value of x-y?
A. 2
B. 5
C. 4
D. 3
E, 6

Click here to see answer by ikleyn(52748) About Me 

Question 1183891: I am stuck on this problem on my homework and i am not entirely sure where to even start
i sqrt(2)-2-(6-4i sqrt(2))-(5-i sqrt(2))

Click here to see answer by ikleyn(52748) About Me 

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