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Question 1208828: Note:

When I use the word "bar" after the complex number expressions, I simply mean there is a bar over each expression.

Given z = 3 - 4i and w = 8 + 3i, write each expression in the standard form
a + bi.

1. z + z bar

2. w - w bar

Click here to see answer by ikleyn(52752)

Question 1208826: Perform the indicated operation and express your answer in the form a + bi.

sqrt{(4 + 3i)(3i - 4)}
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Question 1208825: Write each expression in the standard form a + bi.

1. i^(-23)

2. (1 + i^3

Click here to see answer by Edwin McCravy(20054)

Question 1208871: . The steamboat traveled down the Ohio River at 22 mph and upstream at 14 mph. What was the steamboat's upstream travel time if it was 4 hours more than the time required to travel the same distance downstream?
Click here to see answer by greenestamps(13195)

Question 1208838: find : int ((cos (x)))^(n) dx from 0 to pi
Click here to see answer by Edwin McCravy(20054)

Question 1208838: find : int ((cos (x)))^(n) dx from 0 to pi
Click here to see answer by ikleyn(52752)

Question 1208884: The steamboat traveled down the Ohio River at 22 mph and upstream at 14 mph. What was the steamboat's upstream travel time if it was 4 hours more than the time required to travel the same distance downstream?
Click here to see answer by KMST(5328)

Question 1208901: How many numbers can be formed with five different digits from {0, 1, 2, 3, 4, 5, 6, 7} that must include the digits 2 and 5 ?
Click here to see answer by Edwin McCravy(20054)

Question 1208916: if z = cot (theta) - i , - pi < theta <0 , find | z |
Click here to see answer by ikleyn(52752)

Question 1208917: The function that can be redefined to be continuous at x= π /2 is ...
1) sqrt(x- π/2)
2) abs(sin(2x))/(2x- π)
3) cos(2x)/(x-π/2)
4) sqrt(cos(x)
Click here to see answer by mccravyedwin(405)

Question 1208976: limit (((ln 2))^(x))/(cos ((pi)/4 sin (3 x))) as x \[LongRightArrow] - \[Infinity] = 0 ( T or F )
Click here to see answer by ikleyn(52752)

Question 1208972: find : limit ((ln (2)))^(x) \[Times] sec ((pi)/4 sin (3 x)) as x \[LongRightArrow] - \[Infinity]
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Question 1209093: 1. In how many ways can 3 male students and 2 female students be seated on 6 chairs arranged in a circle such that no two male students are adjacent?

2. In how many ways can 3 male students and 2 female students be seated on 7 chairs arranged in a circle in the following cases:
1. The female students are adjacent.

2. The male students are adjacent.

3. The male students are adjacent, and the female students are adjacent.

4. No two male students are adjacent.

5. No two female students are adjacent.

Click here to see answer by ikleyn(52752)

Question 1209104: How many ways are there to arrange 4 male students and 3 female students in 10 seats around a circle such that each gender sits together?
Click here to see answer by ikleyn(52752)

Question 1209098: In how many ways can 6 people be arranged to sit around a circular table with 10 chairs?
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Question 1209126: Compute (1 + i) + (2 - i) + (3 + i).
Click here to see answer by mccravyedwin(405)

Question 1209127: Fill in the blanks with real numbers.
(11 - 7i)(2 + i) = ___ + ___ *i
Click here to see answer by math_tutor2020(3816)

Question 1209130: For what real number k is (8 + ki) + (7 - 3i) equal to a real number?
Click here to see answer by mccravyedwin(405)

Question 1209130: For what real number k is (8 + ki) + (7 - 3i) equal to a real number?
Click here to see answer by ikleyn(52752)

Question 1209134: We can represent complex numbers geometrically by plotting them on the "complex plane", just like we plot points on the Cartesian plane. The real part of the complex number is the horizontal coordinate and the imaginary part is the vertical coordinate. So, the complex number 0 is the origin. The number 2-3i is plotted below.

We say that the magnitude of a complex number is the distance from that complex number to the origin in the complex plane. We denote the magnitude of the complex number a+bi as |a+bi|.
Compute |1 + 2i + 3 - i - 4 + 5i|.
Click here to see answer by ikleyn(52752)

Question 1209152: if limit ((1 - cos (2 x) cos (2 kx))/(sin ^2(x))) = 10, then k = .... as x \[LongRightArrow]
Click here to see answer by Edwin McCravy(20054)

Question 1209152: if limit ((1 - cos (2 x) cos (2 kx))/(sin ^2(x))) = 10, then k = .... as x \[LongRightArrow]
Click here to see answer by ikleyn(52752)

Question 1209152: if limit ((1 - cos (2 x) cos (2 kx))/(sin ^2(x))) = 10, then k = .... as x \[LongRightArrow]
Click here to see answer by mccravyedwin(405)

Question 1209161: A student writes the six complex roots of the equation z^6 + 2 = 0 on the blackboard.
At every step, he randomly chooses two numbers a and b from the board, erases them, and replaces them with 3ab − 3a − 3b + 4.
At the end of the fifth step, only one number is left. Find the largest possible value of this number.
Click here to see answer by math_tutor2020(3816)

Question 1209167: The roots of the quadratic equation z^2 + bz + c = 0 are 5 + 3i and -2 + 7i. What is b + c?
Click here to see answer by ikleyn(52752)

Question 1209179: find : limit (| sin (x) - 1|)/(sin (x) - 1) as x \[LongRightArrow] (pi)/2
Click here to see answer by Shin123(626)

Question 1209181: If 2^x = 12 and 6^y = 12, then what is (1/x) + (1/y) equal to?
Click here to see answer by math_tutor2020(3816)

Question 1209178: The function f(x)= sqrt(sin(x)(sin(x) -2)+1) is continuous at x = pi/2. ( true or false) ?

Click here to see answer by ikleyn(52752)

Question 1209180: The function: f(x) = |sin(x) - 1| / (sin(x) - 1)
can be redefined to make it continuous at x= pi/2
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Question 1209163: if f ^(2 n)(x) + ((f (x) - 2))^(2 n) = x ^(2 n), n \[Element] N , then (dx)/(d (f (x))) at f (x) = 1 is ....
Click here to see answer by ikleyn(52752)

Question 1209146: Describe all solutions to z -3w - 2iw + 4iz = -8 where z and w are complex numbers.
Click here to see answer by greenestamps(13195)

Question 1209146: Describe all solutions to z -3w - 2iw + 4iz = -8 where z and w are complex numbers.
Click here to see answer by ikleyn(52752)

Question 1209153: If f(x)= (k+x³sec(x))/(sin(b)×(x-π)) is continuous at x= π, and kb -f(π)= 4(π^(5/ 2) , find the value of b .

Click here to see answer by ikleyn(52752)

Question 1209153: If f(x)= (k+x³sec(x))/(sin(b)×(x-π)) is continuous at x= π, and kb -f(π)= 4(π^(5/ 2) , find the value of b .

Click here to see answer by Edwin McCravy(20054)

Question 1209153: If f(x)= (k+x³sec(x))/(sin(b)×(x-π)) is continuous at x= π, and kb -f(π)= 4(π^(5/ 2) , find the value of b .

Click here to see answer by mccravyedwin(405)

Question 1209153: If f(x)= (k+x³sec(x))/(sin(b)×(x-π)) is continuous at x= π, and kb -f(π)= 4(π^(5/ 2) , find the value of b .

Click here to see answer by AnlytcPhil(1806)

Question 1209184: if y ' = - (y)/(x) then y ^((n)) = (((- 1))^(n) n ! y)/(x ^(n)) , n \[Element] N (true or fals)
Click here to see answer by Edwin McCravy(20054)

Question 1209128: From a point 𝐿 outside a circle, we drew tangents to the circle at points 𝐴 and B. From the same point L, we also drew a secant to the circle passing through points g and D, where point g lies between L and D. We selected apoint k on the chord BD such that the measure of the angle ∠(𝑘𝐴𝐷) = ∠(𝐿𝐵g)
Find the following ratio:Measure of ∠(𝐾𝐵𝐷):Measure of ∠(𝐿𝐴𝑔)
Click here to see answer by greenestamps(13195)

Question 1209189: Find the sum and products of the roots of the equation: 2 y square -10y + 7 = 0
Click here to see answer by ikleyn(52752)

Question 1209132: Fill in the blanks with real numbers:
(sqrt(3) + i) * 6 * (sqrt(2) - sqrt(6)*i) * 6 = ___ + ___ i
Click here to see answer by yurtman(42)

Question 1209231: The number of ways to arrange the seating of four men and their wives around a circle, so that each man remains adjacent to his wife, equals..."
Followed by the multiple-choice options:
48
96
120
384
Click here to see answer by greenestamps(13195)

Question 1209237: Express (15 - 16i)(2 - 3i)$ in standard form.
The standard form of a complex number is the form a + bi, where a and b are real.
Click here to see answer by Edwin McCravy(20054)

Question 1209237: Express (15 - 16i)(2 - 3i)$ in standard form.
The standard form of a complex number is the form a + bi, where a and b are real.
Click here to see answer by math_tutor2020(3816)

Question 1209236: Simplify (1-3i) + (2-i) + (2+i) + (1+3i).
Click here to see answer by ikleyn(52752)

Question 1209238: "In how many ways can 7 students be divided into 3 unordered groups such that one group contains 1 student and the other two groups contain 3 students each?"

Click here to see answer by ikleyn(52752)

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