Questions on Algebra: Complex Numbers answered by real tutors!

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Question 1207482: Write each expression in the standard form a+bi.

How do I simplify i^n when n is a big number?

Two samples:

A. i^14

B. 2i^(8)(2 + i^4)

Click here to see answer by math_tutor2020(3816)

Question 1207483: Simplify the square root. Write your answer in the form a + bi.

sqrt{(4 + 3i)(3i - 4)}

Do I FOIL the radicand?
Click here to see answer by math_tutor2020(3816)

Question 1207483: Simplify the square root. Write your answer in the form a + bi.

sqrt{(4 + 3i)(3i - 4)}

Do I FOIL the radicand?
Click here to see answer by ikleyn(52747)

Question 1207483: Simplify the square root. Write your answer in the form a + bi.

sqrt{(4 + 3i)(3i - 4)}

Do I FOIL the radicand?
Click here to see answer by MathTherapy(10549)

Question 1207484: Solve each equation in the complex number system.

A. x^4 = 1

B. x^4 + 3x^2 - 4 = 0
Click here to see answer by math_tutor2020(3816)

Question 1207485: find the Domain of f(x) = sqrt(sec (x))
Click here to see answer by ikleyn(52747)

Question 1207534: if f (x) + f '' (x) = 2 tan ^3(x) + tan ^2(x) + tan (x) + 1 , then f (x) = ...
Click here to see answer by mccravyedwin(405)

Question 1207569: Finding the Principal Root of a Complex Number
(-8i)^(1/3)

Click here to see answer by greenestamps(13195)

Question 1207602: Write each expression in the form a + bi.

1. i^(15)

2. 2(i^4)(1 + i^2)
Click here to see answer by ikleyn(52747)

Question 1207602: Write each expression in the form a + bi.

1. i^(15)

2. 2(i^4)(1 + i^2)
Click here to see answer by math_tutor2020(3816)

Question 1207602: Write each expression in the form a + bi.

1. i^(15)

2. 2(i^4)(1 + i^2)
Click here to see answer by Edwin McCravy(20054)

Question 1207605:
Click here to see answer by josgarithmetic(39613)

Question 1207604: Without solving, determine the character of the solutions of each equation in the complex number system.

1. 2x^2 - 4x + 1 = 0

2. x^2 + 6 = 2x
Click here to see answer by ikleyn(52747)

Question 1207603: Solve each equation in the complex number system.

1. x^4 = 16

2. x^4 + 13x^2 + 36 = 0
Click here to see answer by MathLover1(20849)

Question 1207603: Solve each equation in the complex number system.

1. x^4 = 16

2. x^4 + 13x^2 + 36 = 0
Click here to see answer by greenestamps(13195)

Question 1207629: Write each expression in the form a + bi.
1. 2i(i^(-3))

2. 2i(i^(-3)) ÷ i^(-4)
Click here to see answer by MathLover1(20849)

Question 1207638: if f (x) = ((sqrt(x)))^2 , g (x) = x then f (x) = g (x) True or false
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Question 1207763: if f (x) = |(x + 1)((x - 5))^2| , find , f '(- 1) , f '(5)
Click here to see answer by ikleyn(52747)

Question 1207776: How many random ways can a 20-question multiple-choice test be answered, with each question having 4 options?
Click here to see answer by math_tutor2020(3816)

Question 1207776: How many random ways can a 20-question multiple-choice test be answered, with each question having 4 options?
Click here to see answer by ikleyn(52747)

Question 1207774: int x ^((x)/(ln x)) from 0 to 1 dx
Click here to see answer by mccravyedwin(405)

Question 1207779: Let z and w be complex numbers such that |z| = |w| = 1 and zw is not equal to -1.
(a) Prove that conjugate {z} = 1/z and conjugate{w} = 1/w
(b) Prove that ={z + w}/{zw + 1} is a real number.

Click here to see answer by ikleyn(52747)

Question 1207796: i² = -1 , if n \[Element] Z then i ^(2 n + 1) = \[PlusMinus] i (T or F)
Click here to see answer by greenestamps(13195)

Question 1207809: 67 54 71 03 22
61 97 38 01 79
63 90 85 64 58
55 44 11 87 14
11 66 40 44 40
67 20 32 86 67
03 98 80 20 29
54 81 04 97 46
39 36 58 32 74
19 67 68 32 65
46 25 91 51 22
35 13 11 18 65
48 93 52 97 97
32 50 47
Click here to see answer by math_tutor2020(3816)

Question 1207844: Let A = {n ∈ Z | |n| ≤ 24}. In how many ways can two distinct numbers be chosen (simultaneously) from A such that their product is less than their sum?
Click here to see answer by ikleyn(52747)

Question 1207847: If |x-6|+|x-5|+|x-4|+...+|x+5|+|x+6|= m ,then m = ...
[ 36 ,38 ,40 ,42 ,44 ]
Click here to see answer by ikleyn(52747)

Question 1207846: If |x-1|+|2x-2|+|3x-3|+...+|nx-n|=750 ,then x=...
A)4024
B)2012
C)1006
D)100
E) 2
Click here to see answer by ikleyn(52747)

Question 1208001: if f (x) = 1/(1 - x) , then (f(f(f(f...f)(sqrt2),(45 times) = ...., A) 0, B)(2 - sqrt2)/2, C)(2 + sqrt2)/2, D) 1, E) sqrt2
Click here to see answer by mccravyedwin(405)

Question 1208001: if f (x) = 1/(1 - x) , then (f(f(f(f...f)(sqrt2),(45 times) = ...., A) 0, B)(2 - sqrt2)/2, C)(2 + sqrt2)/2, D) 1, E) sqrt2
Click here to see answer by ikleyn(52747)

Question 1208183: If f(x)= 1/((1/x)-3) , find the domain of f(f(x))
Click here to see answer by ikleyn(52747)

Question 1208190: Let S={1,2,3,4,…,n}, and let A and B be two subsets of S such that A ≠ ∅, B ≠ S, and A ⊆ B.
Calculate the number of ordered pairs (A,B) for all subsets of the set S
Click here to see answer by ikleyn(52747)

Question 1208189: How many possible are there to place two queens on an empty chessboard such that neither threatens the other?
Click here to see answer by PPCHLOE(2)

Question 1208189: How many possible are there to place two queens on an empty chessboard such that neither threatens the other?
Click here to see answer by ikleyn(52747)

Question 1208189: How many possible are there to place two queens on an empty chessboard such that neither threatens the other?
Click here to see answer by mccravyedwin(405)

Question 1208213: if y = sin (t) , x = ln (t) , then ,(d ^2 y)/(dx ^2)=... when (x = π)
Click here to see answer by math_tutor2020(3816)

Question 1208213: if y = sin (t) , x = ln (t) , then ,(d ^2 y)/(dx ^2)=... when (x = π)
Click here to see answer by ikleyn(52747)

Question 1208213: if y = sin (t) , x = ln (t) , then ,(d ^2 y)/(dx ^2)=... when (x = π)
Click here to see answer by mccravyedwin(405)

Question 1208215: if y = sin (t) , x = ln (t) , then ,(d ^2 y)/(dx ^2)=... when (t = π)
Click here to see answer by ikleyn(52747)

Question 1208214: if dy/dx = sec(x) , dt/dx = tan(x) - 3, then ,(d ^2 y)/(dt ^2) =... when(x = 0
Click here to see answer by mccravyedwin(405)

Question 1208237: Find the domain if f(x) = x^x
Click here to see answer by ikleyn(52747)

Question 1208240: if f (f (x)) = x ^2 - x + 1, find f (x)
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