Let w e H and suppose that (1+ i)w(1+ 2j) = 1+ k. nd w (your answer should be in the form a + bi + cj + dk).

Q: 5. Determine given: axty - bxy = 36 %3D where a and b are constants.

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Q: If f = xi + yj + zk, l7I = r,and i=, then show that grad () =

A: 1. Gradf=(dfdxi^ + dfdyj^ + dfdzk^ )      2.  dxndx = n xn-1 3. r = x2+ y2 +z2

Q: Given z = -5+ 3i and z2 = 3 – 6i, express in the form a + bi %3D i. 4z1* – Z2 ii. Z2

A: Complex Cartesian form

Q: If Z= 3 – 2i and W = 4 – I, write  ZW in the form a + bi

A: Z=3-2i  &  W=4-i

Q: Let x, y, z e Z Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

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Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

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Q: Say that E = Ãek™, where the components of A and k are real and constant, i.e. they aren't imaginary…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) - then the domain of r is О 11, 10] (1, 0) O [1, 10) O…

A: Explanation of the answer is as follows

Q: Complete the proof that ZYXZ SUT. P Q R. U W Y

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Q: Let R be and bl#0) = iff a with unity - Let a l#0) in R- Show that and b an I.D are are associates-

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Q: Solve the following forr W=4xc for c %3D C = (Type an exact

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Q: Complete the proof that AUVX ATWX. U V T. W

A: Given:  WX=VX and UX=TX. In △UVX and △TWX WX=VX                  (Given) UX=TX…

Q: If r(t) = (e³t, e-4t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = II T(0) = r"(0) =…

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Q: Given z = 3– 4i and w = -1- 2i, compute the following and express your final answers in the fe-n a +…

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Q: 2. Given: XW XY, HA I WY, KB 1 WY Prove: AHWA ~ AKYB. K Y.

A: Given data is : XW¯≅XY¯ Therefore ,  ∠XWY≅∠XYW∠XWY≅∠HWA∠XYW≅∠KYBTherefore,∠HWA≅∠KYB     .....1…

Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: 6. Let a, b e Rwith b + 0. Show that R(a + bi) = C. %3D

A: We have to show that R(a+bi)=C. We prove it in two oashow that R(a+bi) is a subset of C and C is a…

Q: Find the imaginary component of In(2z + w) if z = 11 + 9i and w=10+4i .

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Q: m is the mid point of AB find a Of AM

A: Equating the given relation gives the value of x . Then substituting the value of x in the…

Q: Use the substitution x = et, to solve the following Cauchy-Euler equation: x²y// – 4xy/ + 4y = x³ In…

A: We will find out the required solution for given Cauchy Euler differential equation.

Q: Suppose AE R, v#0, and (A- A)v#0. Use the fact that A is symmetric show that it is impossible to…

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Q: Let r,s,t,u be the roots of the equation x* + Ax + Bx + Cx +D = 0. Prove that, if rs = tu, then A D=…

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Q: One of the following has only one nilpotent element Z[i] = {a + bi : a, b E Z} M2x2(2Z) ZOZO Z6

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Q: Prove that I(x)l(m) Bim, m) = for m > 0 2r(m+

A: We use the definition and properties of Beta and Gamma functions to prove the given result.

Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate w when…

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Q: Solve the following P.D.E. , with the following conditions: u(0,y) = 0, u(L,y) = 0, u(x,0) = 0 and…

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Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: Let a,b E R with a # 0, b # 0. Prove that (ab)¯1 = a°1b´1. %3D

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Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

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Q: In the given figure, X > K. Prove that WY> JL. K X Y W

A: Here , we have ∠X>∠K we have to prove that WY>JL

Q: Determine the real number \( \alpha \) u x v and î are orthogonal, where ù = 3î + ĵ– 5k and v = 4î –…

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Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: Find the gene ral solution of the following DESI XY +y² - x? y' = o %3D

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Q: Verify by direct substitution that Un(x,y)=sinnx sinhny is a solution of Uxx+Uyy=0 for every n>0.

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Q: Suppose T(z) = Find a solution to T(x) = | %3! in terms of z. Note: We are using T : C → R? such…

A: The function T is defined from complex plane to cartesian plane. T(a+bi)=a-b0.  Given the line in…

Q: IF| = r r) = -i = 5xi + 2yj – 2zk so be it where div() , grad(f find all of

A: Solution:

Q: Let  V = −4i + j  and  W = i − 4j,  and find the following. |3V − W|

A: V = −4i + j W = i−4j   3V = 3(−4i + j) 3V = -12i + 3j So, 3V − W = -12i + 3j - ( i−4j )…

Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: Write a in the form of a = a„T+a„N at t = 0 without finding T and N first if r(1)=(2+3¢+ 3¢°)i+(4+…

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Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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Q: of the following conditions imply that B = se, either prove or give a counterexample. B] AUB = AUC…

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Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

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Q: Q2= A) for E- 2x1-3Y3+K prove That div( curl È)=0 B Find A and M if (21+bj+27k) X (i+Ai+Mk)=0 I uck

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Q: D B. E C Given: AB XEB = CB × DB Prove: AABC- ADBE

A: To Determine: prove △ABC~△DBE Given: we have a figure in which we have triangles △ABC and △DBE also…

Q: Which of the following is a general solution to the followin x²y"+xy'+ (x²– 1)y=0 y=c,(x) +cY_,(x) O…

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