Questions on Algebra: Complex Numbers answered by real tutors!

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Question 1112640: I have a problem I'm not sure I solved right
-4+1i/3i
What I did was (-4+1i/3i)(i/i) = -4+1/3 = -3/3 = -1
Is this correct?
Click here to see answer by MathTherapy(10549)

Question 1112642: Divide: 1-4i/5-6i. Write your answer in a+bi form
A=
B=
I'm really confused on the a+bi thing, as well as solving the fraction. I tried to cancel out the i's, but I think that's the opposite of what I'm supposed to do.
Click here to see answer by ikleyn(52747)

Question 1112639: -4+4i how would I solve this?
Click here to see answer by math_helper(2461)

Question 1112684: what is negative one to the third power
Click here to see answer by Alan3354(69443)

Question 1112754: Why i ^ (-1) = -1 ?
Click here to see answer by ikleyn(52747)

Question 1112851: Isaac made all these rectangles with 24cm lengths of string.This implies that the perimeters of all the rectangles are equal.
Click here to see answer by josgarithmetic(39613)

Question 1112924: Round 8.1845062 to the nearest hundred-thousandths
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Question 1112924: Round 8.1845062 to the nearest hundred-thousandths
Click here to see answer by josmiceli(19441)

Question 1113011: please solve 5/-2 + 5i
-2/-2 (5/-2 + 5i)
1/-2 ( 5/ 5i)
1/-2 ( 1/ i )
1/ -2i
2/2 ( 1 / -2i )
? I'm lost from here ? 2 /-i ?

Click here to see answer by solver91311(24713)

Question 1113091: someone help me? Thank you.
Q: What is the trignometric form of the complex number w=-3+i?

Click here to see answer by amalm06(224)

Question 1113095: can someone help me plz? Thank you. What is the trigonometric form of the complex number w=-3+2i?

Click here to see answer by rothauserc(4718)

Question 1113136: someone help please. Convert the equation r=12/(3cos theta+4sin theta) from polar form to rectangular form. Thank you.
Click here to see answer by ikleyn(52747)

Question 1113137: Please help me. How to prove that log b x- log b y = log b (x/y). (* "b" should be smaller letter)
Thank you.
Click here to see answer by math_helper(2461)

Question 1113135: can someone help please? Convert the point (-6,-6) from rectangular form to polar form. Thank you.
Click here to see answer by Theo(13342)

Question 1113301: Carlos is 7 years older than tom. find their ages when 1/4 of Carlos's age is equal to the 1/2 of tom's age ?
Click here to see answer by josgarithmetic(39613)

Question 1113676: 1/z = 1/(2 + i) + 1/(-2 + 4i), evaluate z in the form x + iy
Click here to see answer by math_helper(2461)

Question 1113675: Solve for x and y, 3x + iy = (1 + i)(x^2 + y^2). Ans: x = 3/10 and y = 9/10
Click here to see answer by math_helper(2461)

Question 1113677: Given that √(x + iy) = a + ib, so that x = a^2 + b^2, y = 2ab and find a and b if x = 3, y = 4
Click here to see answer by ikleyn(52747)

Question 1113734: 3 = a^2 - b^2 and 4 = 2ab, find a and b
Click here to see answer by Alan3354(69443)

Question 1113737: What is (1+i)^12 in standard form using De Moivre's Theorem

Click here to see answer by Alan3354(69443)

Question 1113738: Does [sqrt2(cos(x)+i*sin(x))]^12 = 64(cos(12x)+i*sin(12x))? If not how would the exponent of 12 be applied to the following: [sqrt2(cos(x)+i*sin(x))]^12 ?
Click here to see answer by ikleyn(52747)

Question 237884: Prove how 3 is irrational
Click here to see answer by amalm06(224)

Question 237884: Prove how 3 is irrational
Click here to see answer by Shin123(626)

Question 1113877: Given x≡19(mod5)
Identify which one of the following options gives integers that are valid solutions for x ?

-19 and 7

-11 and 54

7 and 26

11 and 26

Click here to see answer by ikleyn(52747)

Question 1113998: Given
Amod7=5

Bmod7=6

(A+B)mod7=Y

Identify which one of the following options is a valid solution for Y ?

-4

5

4

-7

Click here to see answer by rothauserc(4718)

Question 1114082: 9^563 mod907

Here is my working so far.
1) Firstly, because the power is not 2, I had to find the powers of 2 that add up to the exponent.
29 = 512 25 32 24 =16 21 =2 20 1
512+32+16+2+1=563
so k =(0,1,4,5,9)
2)Calculate 92 k for 0,1,4,5,9
Where k =0 91 mod 907 = 9
ANS =9
Where k=1
81 mod 907 = 81
Where k=4
94=6561 / 907 = 7.2337
7*907 = 6349 so 6561 -6349 =212
ANS =212
95 =59049
59049/907 =65
65*907 = 58955
59049-58955=94
ANS = 94
99 =386420489 386420489 /907 =427144
427144*907=387419608
387420489-387419608=881
ANS =881
3) Multiply all the ANS together...
so...
881 x 94 x 212 x 9x 81
=158009112 mod 907
=158009112 / 907
=174210
158009112 - 158008470 = 642
ANS =642
However, the answers are:
310
520
630
493
Where have I went wrong
Click here to see answer by rothauserc(4718)

Question 1114095: Find a polynomial equation with roots 3 + 2i, 1/2
Click here to see answer by josgarithmetic(39613)

Question 1114096: Write -(-3 + 7i) + (-6 + 6i) in the form (x, y)
Click here to see answer by Fombitz(32388)

Question 1114091: Show that the polynomial f(z) = z^2 + 3/4z + 7 is factorizable over the complex field but not factorizable over real field
Click here to see answer by amalm06(224)

Question 1114161: (-4+7i)+(5-10i)

Click here to see answer by Alan3354(69443)

Question 1114840: Express in standard form:
Click here to see answer by ikleyn(52747)

Question 1114841: Express in standard form:
Click here to see answer by MathLover1(20849)

Question 1115020: Let z=a+bi. Discuss the values of a and b so that the following will be true:
z(i) is a positive real number and z(3-i) is a pure imaginary number.
Click here to see answer by Fombitz(32388)

Question 1115576: Please help me solve the following problem
Find all the values of z such that

My attempt at a solution.

Pairing the real and imaginary parts gives
----------- (1)
and
----------- (2)
Then

since Im trying to find a value of of y such that

and

Therefore,
but the book gives the answer as so I know I'm messing up the imaginary part I'm just not sure how .

Click here to see answer by math_helper(2461)

Question 1116180: Solve for x and y in (2x-y)+(x+y)i=6i
Kindly show the solutions please. Thank you
Click here to see answer by josgarithmetic(39613)

Question 1116154: How do I find all the values to the following?
1) i^0.25
2) (1+sqrt(3)i)^(1/3)
3) (i-1)^0.5
4) ((9i)/(1+i))^(1/6)
Click here to see answer by KMST(5328)

Question 1116384: Use the complex number cosx + isinx to find the constants A, B, C in the identity
cos4x = Acos^4x + Bcos^2xSin^2x + Csin^4x

Click here to see answer by ikleyn(52747)

Question 1116382: (z-1)/(z+1) = ki
show |z| = 1

Click here to see answer by ikleyn(52747)

Question 1116415: let z be a complex number with arg(z)=theta and |z|=k
find the following:
i) arg(2z)
ii) |z| bar
iii) |z^2|/|z| bar
iv) arg(z bar * z^2)

Click here to see answer by ikleyn(52747)

Question 1116414: find all the solutions in the complex numbers, of z^4 + z^3 + z^2 + z + 1 = 0.
use: (1-r)(1+r+r^2+...+r^n)=1-r^(n+1)
which of the solutions are conjugates?
Click here to see answer by ikleyn(52747)

Question 1116926: Why might one prefer to use the chain rule for dealing with high degree functions, such as (x+1)^9?

Click here to see answer by solver91311(24713)

Question 1117174: The sequence of numbers 12345678910111213. . . 997998999 is found by writing the numbers 1, 2, 3, . . ., 999 in order. What would be the 1997th digit (from the left) of the lengthy number?
Click here to see answer by ikleyn(52747)

Question 1117251: Write a quardratic in standard form with the root 3,-4

(2) -7,3/4
Click here to see answer by stanbon(75887)

Question 1117501: -7i + 0i. Please explain it's additive inverse
Click here to see answer by math_helper(2461)

Question 1117501: -7i + 0i. Please explain it's additive inverse
Click here to see answer by Alan3354(69443)

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