Given a=9i - 5j and b=7i - 4j, express i and j in terms of a and b.?
483123
a = 9i - 5j\nb = 71 - 4j\n\nq1\n\na + 5j = 9i\nb + 4j = 7i\n\n(b + 4j) / 7 = i\n(a + 5j) / 9 = i\n\ntherefore:  (b + 4j) / 7  = (a + 5j) /9\ncross multiply\n9b + 36j = 7a + 35j\n36j - 35j = 7a - 9b\n\nj = 7a - 9b.  ans1\n\nQ2\n\na - 9i = -5j\nb - 7i = -4j\n\nfollow same process as above  (dive both sides number functions,  then cross multiply)\n\n4a - 36i = 5b - 35i\n\n-35i + 36i = 4a - 5b\n\ni = 4a - 5b\n\n\nConclusion\n\nj = 7a - 9b\n\ni = 4a - 5b
643397
(8y^3 + 27)/(2xy - 10y + 3x - 15)\n((2y + 3)(4y^2 - 6y + 9))/((2xy - 10y) + (3x - 15))\n((2y + 3)(4y^2 - 6y + 9))/(2y(x - 5) + 3(x - 5))\n((2y + 3)(4y^2 - 6y + 9))/((2y + 3)(x - 5))\nthe (2y + 3)s cancel out\n(4y^2 - 6y + 9)/(x - 5)\n\nANS : (4y^2 - 6y + 9)/(x - 5)
949749
m=cab/a-b\n\nMultiply both sides with (a-b) you would get\nma-mb=cab\ni.e. cab+mb=ma\n      b(ca+m)=ma\ngiving you b=ma/ca+m
815598
a+b+ c+ab+cb+ac = abc + 1\nor a+b+c - abc = 1- ab-cb-ac\nor (a+b+c - abc)/(1-ab-bc-ac) = 1\n\nputting a = TAN A , b= tan B, c = tan C\n\nwe get LHS = tan(A+B+C) = 1\nor A+B+C = tan ^-1 = pi/4+npi\n\n chose any a and b then c can be chosen as\n\ntan^1(pi/4 - tan A - tan B)
586962
(6y^2-3y)(y+7)-->(2y)(y-1)(y+7)\nif that helps
572398
first multiply i by everything in the first bracket.\nso -8i * i + 3 * i + 2(2-5i)\n\nthen do same with 2nd bracket\nso -8i^2 + 3i + 2*2 - 5i*2\n= -8i^2 + 3i + 4 - 10i\n\nnow collect all the like terms\n-8i^2 + 3i - 10i + 4\n= -8i^2 - 7i + 4\n\nnow if i is the imaginary number i^2 would be -1.\nso it would be 8-7i +4 = 12-7i\n\nhope that helps. laterz
830360
9x-(-2x) = 5x+4x-{2(x-10+3+7)}(-1) = 5x +2x-11x+22x-5x-x+x(-1)\n\n= 11x
869966
http://www.math.psu.edu/tseng/class/Math140H/Sqrti.html\n\nAnd, BTW, i (or j) is not a 'complex' operator.  It is the 'imaginary unit' ☺\n\n\nDoug
272561
1 b = 5\n2 c = 7\n3 c = -8\n4 b = 9
496037
-3x + 5y = 8\nx + 2y = 1\n\n(-3x + 5y) + (x + 2y) = 8 + 1\n-3x + 5y + x + 2y = 9\n-2x + 7y = 9\n\n7y = 2x + 9\ny = (2/7)x + (9/7)\n\nx + 2y = 1\nx + 2((2/7)x + (9/7)) = 1\nx + (4/7)x + (18/7) = 1\n7x + 4x + 18 = 7\n11x + 18 = 7\n11x = -11\nx = -1\n\ny = (2/7)x + (9/7)\ny = (2/7)(-1) + (9/7)\ny = (-2 + 9)/7\ny = (7/7)\ny = 1\n\nx = -1\ny = 1
791337
1) (1/2 i+2bj) - (bi-b^2 j) + ((7/2 +b)i-bj) = 4i+20j\n\nNow separate the equation into two equations.\n\n1/2 i - bi + (7/2 + b)i = 4 i\n2bj + b^2 j - bj = 20j\n\ni and j are no longer needed so get rid of them too\n\n1/2 - b + 7/2 + b = 4 => 0 = 0 (Not a big help)\n2b + b^2 - b = 20 \n\nb^2 + b - 20 = 0\n\nTime for the quadratic formula.\n\nb = (-1 +- sqrt(1 + 80)) / 2 = -1/2 +- 9/2 = -5, 4\n\n2) x = 1/2 i+2bj\n\nBasically you need to find where b makes the length of the vector equal to one. The Pythagorean Theorem helps here.\n\n(1/2)^2 + (2b)^2 = 1^2\nb = sqrt(3/4) / 2
904926
5+-V92\nquadratic formula
558121
i=i+2 (i=4)\ni++ (i=5)\ni=5
464606
Simplify: (14-5i)+(-8+19i)\n\nStrategy: Remove the ( ) and then combine the parts without an i (the "real" terms) and then combine the parts with an i (the "imaginary" terms). You are adding complex numbers in this problem.\n\nSolution:\n(14-5i)+(-8+19i)\n = 14 - 5i - 8 + 19i\n = 14 - 8 - 5i + 19i\n = 6 + 14i\n\n \nSimplify: (7+3i)(7-3i)\n\nStrategy: Remove the ( ) by applying the "FOIL" method (a.k.a. Distributive Property of Multiplication over Addition). We will also use the definition i^2 = -1 to complete the simplification. You are multiplying complex numbers in this problem.\n\nSolution: \n(7+3i)(7-3i)\n = 49 - 21i + 21i - 9i^2\n = 49 - 9i^2\n = 49 - 9(-1)\n = 49 + 9\n = 58\n\nNote: You may also write the answer in complex form (a + bi) as 58 + 0i.
75797
5*60/40 = J, 7.5\n\nThanks for stimulating my brain for a couple of seconds.
926657
(3 a^-7 b^7) / (9 a^7 b^-5) = ((3)(1/a^7)(b^7)) / ((9)(a^7)(1/b^5)) =\n\n((3 b^7) / a^7) / ((9 a^7) / b^5) = ((3 b^7) / a^7) times (b^5 / (9 a^7))\n\n= (b^12) / (3 a^14)    OR    3^-1 a^-14 b^12
650764
Remember that i^2 is -1 so\n-3i+2(-1)-2+i=-4-2i