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Question 1102414: Evaluate: 𝑛^5 − 4𝑝^0 + (𝑝 − 𝑛)^2 − 𝑝𝑛 if 𝑛 = −2 and 𝑝 = 3
Click here to see answer by Boreal(15235)

Question 1102415: 8𝑏𝑐 − 4𝑐𝑥^2 + 52𝑐

Click here to see answer by Alan3354(69443)

Question 1102412: (0.00008 � 10^4) (100, 000 � 10^−2)
(40 � 10^3) (0.02 � 10^−2)

Click here to see answer by Alan3354(69443)

Question 1102412: (0.00008 � 10^4) (100, 000 � 10^−2)
(40 � 10^3) (0.02 � 10^−2)

Click here to see answer by josgarithmetic(39617)

Question 1102411: Add: 𝑝𝑞^2/𝑧 − 𝑞 + 𝑧^2𝑝^2/𝑞
Click here to see answer by Alan3354(69443)

Question 1102413: 𝑥/4 + 2x-1/12 =-3

Click here to see answer by Alan3354(69443)

Question 1102471: The equation 𝑧^2 = −5 + 12𝑖 has two (complex) solutions. Note that
𝑧 = sqrt (−5 + 12𝑖)is not a particularly useful way to write a solution, since it does not tell us the real and imaginary parts of the solution. We are actually trying to find solutions in the form 𝑧 = 𝑥 + 𝑖𝑦. Show that 𝑧 = 2 + 3𝑖 is such a solution and find the second solution. I know how to prove that z= 2 +3i is a solution, but I just don't know how to find the other solution? Please explain!
Click here to see answer by rothauserc(4718)

Question 1102474: the function �sgn b�, called the signum function, which is Latin for �sign�. For the purpose of this problem, we will define this function as follows:
sgnb={−1, b<0 } (the bracket should cover the whole thing)
{ 1, b≥0 }
For example, sgn(17) = 1, sgn(−√2) = −1, and sgn(0) = 1.
d) If b is any real number, how does the expression |b| sgn b simplify? Explain briefly.

Click here to see answer by KMST(5328)

Question 1102473: For each statement,state whether it is always,sometimes,or never true, and briefly justify each answer:
N) If 𝑞 ∈ N, then there exists a number 𝑝 ∈ N such that 𝑝2 = 𝑞.
Z) If 𝑞 ∈ Z, then there exists a number 𝑝 ∈ Z such that 𝑝2 = 𝑞.
Q) If 𝑞 ∈ Q, then there exists a number 𝑝 ∈ Q such that 𝑝2 = 𝑞.
R) If 𝑞 ∈ R, then there exists a number 𝑝 ∈ R such that 𝑝2 = 𝑞.
C) If 𝑞 ∈ C, then there exists a number 𝑝 ∈ C such that 𝑝2 = 𝑞.
Click here to see answer by KMST(5328)

Question 1102479: Is there a complex number solution to:
arccos(x) = 2 ?
Click here to see answer by stanbon(75887)

Question 1102479: Is there a complex number solution to:
arccos(x) = 2 ?
Click here to see answer by ikleyn(52786)

Question 1102517: cos(x) = 2
Solve for x, a complex number.

Click here to see answer by stanbon(75887)

Question 1102550: I've forgotten how to do this.
----
cos(x) = 2
Solve for x.
-------------
As an example from my book:
cos(+/-arctan(2sqrt(6)/5) - i*ln(7) + n*2pi) = 10
=======================================================
--> cos(x) = 10
x = +/-arctan(2sqrt(6)/5) - i*ln(7) + n*2pi

Click here to see answer by math_helper(2461)

Question 1102568: Ref # 1102550
----------
cos(x) = 2
Solve for x.
-------------
As an example from my book:
cos(+/-arctan(2sqrt(6)/5) - i*ln(7) + n*2pi) = 10
=======================================================
--> cos(x) = 10
x = +/-arctan(2sqrt(6)/5) - i*ln(7) + n*2pi
============================
If cos(x) = 10 has a solution,
I think cos(x) = 2 does also.
I solved that years ago, but I don't remember how to do it now.
I will figure it out, with or without help.
================
Then I wonder about cos(x) = 2 + i ???

Click here to see answer by rothauserc(4718)

Question 1102975: (2+3i) (3-2i)

Click here to see answer by greenestamps(13200)

Question 1103181: An exam has 5 True and False questions, followed by 6 multiple choice questions each with 4 possible answers (A, B, C, or D). Suppose the student might leave questions unanswered, and for the multiple choice questions, choose at most one of the options.
How many different answer sheets can you get from such exam?
Click here to see answer by Boreal(15235)

Question 1103892: A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?
Click here to see answer by josgarithmetic(39617)

Question 1103906: 13 Z +4 -Z +5Z +2
Click here to see answer by Alan3354(69443)

Question 1103991: prove |z^2|=|z|^2

Click here to see answer by Fombitz(32388)

Question 1104065: find all solution of 2*z^4-3*z^3-7*z^2-8*z+6=0
Click here to see answer by ikleyn(52786)

Question 1104068: determine all the indicated roots and represent them graphically :
a) (4*sqr(2)+4*sqr(2i))^1/3
Click here to see answer by greenestamps(13200)

Question 1104074: if w=f(z)=z+1/z.......for what finite values of z is f(z) non-analytic?
Click here to see answer by ikleyn(52786)

Question 1104077: Given the function w=z^4.
a) show that the Rauchy Riemann equation hold at all point in the finite z plane
b) prove that u and v are harmonic function
please I want some explanation in the answer
thank you very much..
Click here to see answer by richwmiller(17219)

Question 1104069: determine all the indicated roots and represent them graphically :
a) (4*√2+4*√2i)^1/3
Click here to see answer by KMST(5328)

Question 1104083: Given the function w=z^4.
a) show that the Rauchy Riemann equation hold at all point in the finite z plane
b) prove that u and v are harmonic function
please I want some explanation in the answer
thank you very much..
Click here to see answer by richwmiller(17219)

Question 1104164: Let a,b,c be integers such that a^2+b^2 = c^2.
For c divisible by 3, prove that a and b are both divisible by 3 by using congruences.
Click here to see answer by ikleyn(52786)

Question 1104210: prove |z1 - z2|
Click here to see answer by richwmiller(17219)

Question 1104209: prove |z1 + z2+ z3|
Click here to see answer by richwmiller(17219)

Question 1104208: prove |z1 + z2|
Click here to see answer by richwmiller(17219)

Question 1104570: Find the values of x and y for which the equation is true.
(x+4y)+(2x-3y)i=13+7i
Click here to see answer by josgarithmetic(39617)

Question 1104383: Prove |z1/z2|=|z1|/|z2| without using the polar form.
Click here to see answer by math_helper(2461)

Question 1104804: z = a + bi ---- a complex number.
sin(z) = 2
Solve for z.

Click here to see answer by Alan3354(69443)

Question 1104919: Find the values of k, for which the equation kx^2+6x+k=0, has conjugate imaginary roots.
Click here to see answer by greenestamps(13200)

Question 1104828: prove that if z1 z2 z3 are complex numbers on the unit circle such that z1+z2+z3=0, then z1 z2 z3 are vertices of an equilateral triangle
Click here to see answer by greenestamps(13200)

Question 1104943: Hi,
I am reviewing for my final and need help. Please show me what I did wrong on the following question.
8+7i
-----
3-4i
That is a fraction and the question is asking to put it into standard form.
I multiplied both top and bottom by (3+4i) and got -4+53i for top and 25 for bottom. I have redone this problem several times and keep coming up with the same answer. The answer choices are 4/25+53/25i (what I chose), 52/7-11/7i, 52/7+53/7i, and 4/25-11/25i
Thanks in advance!

Click here to see answer by Alan3354(69443)

Question 1105029: x^5-3x^3-4x=0
solve under the set of complex numbers
Click here to see answer by Alan3354(69443)

Question 1105039: The length of a rectangle is 1 less than twice the width.
The area of the rectangle is 28 square feet.
How do you represent the situation?
Click here to see answer by Alan3354(69443)

Question 1105418: Suppose w is a cube root of unity with w not equal to 1 suppose P and Q are the points on complex plane defined by w and (w^2) if O is the origin then what is angle between OP and OQ
Sir solve this problem from easy mathod
Click here to see answer by Alan3354(69443)

Question 1104562: x = cos(1 + i)
Solve for x.
Click here to see answer by rothauserc(4718)

Question 1105620: Find the real numbers x and y that make the equation true.
-4 + yi = x + 3i
Click here to see answer by josgarithmetic(39617)

Question 1105809: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, -13, and 5 + 4i
Click here to see answer by Boreal(15235)

Question 1106095: A two digit number whose ten digit is 2 more than the units digit is 3 more than 6 times the sum of its digits. Find the original number
Click here to see answer by greenestamps(13200)

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