State De Moivre's theorem and if z 7+ j4, find z5 using the ( theorem.

Q: Kis the midpoint of GI and FJ. Complete the proof that AGJK = AIHK. H G

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Q: A. State De Moivre's theorem and if z 7+ j4, find z using the theorem.

A: De Moivre's theorem states that: cosθ+isinθn=cosnθ+isinnθ for all integers n. Also, it extends to:…

Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

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Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: Let xe c and ye show that <xiy= y AX is qu inmer product if A is hermition positive del iniite

A: (Solving the only one question as per our guidelines) Question: Let x∈ℂm and y∈ℂm Show that x,y=y*Ax…

Q: ?, R(A)IN(A*)

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Q: Find the Ker(T) and Rng(T) and their dimensions. T:R → R defined by T(x)= Ax , where 1 -1 A = -3 3…

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Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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Q: Given: ZG = ZI , FH bisects ZGFI Prove: GF = IF G F

A: If all the angles of two triangles are equal, the triangles are said to be congruent.

Q: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: Select all of the statements that are true. DG = 8 %3D AG = 10 GE = 10 %3D O CG = CD O G is the…

A: Given, Also given, AE=15AF=8FG=6BF=24

Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

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Q: Given z = 3 cis 120°, find z3 using De Moivre's Theorem.

A: We have to simplify

Q: Can there exist a AROS in which the trisectors of 20 intersect RS at D and E, with RD = 1, DE = 2.…

A: Given: ∠O intersect RS  at D and E in a △ROSwith the data  RD=1;   DE=2;…

Q: Drag the postulate or theorem that proves the trieng AZWX AY XW a. ATSU AXVW # SSS E SAS

A: which criteria follow to congruent triangle

Q: Evaluate fr z sin(z2) dz where I is the union of the directed line segment that joins the origin to…

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Q: z is a complex variable z=x+iy pic attached with question

A: To analyze and classify the singular points of the given function of the complex variable z

Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

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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: Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: Given z = -2V2 – 2/2i, find z* using De Moivre's Theorem.

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Q: State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for…

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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: Given: ZG = ZI, FH bisects ZGFI Prove: GF = IF H

A: Given that ∠G≅∠I FH bisects ∠GFI To prove that GF≅IF

Q: graup Consider a dibedral 2. Du= carb: d=b-(ab)"%=D1> Discuss all passible Commulators 'and verify…

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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: 1 1 b. From (i) prove that, xb + x ² + 1 + x² + x ² + 1 ² + 1 = 1 xa +x+b+1 c. From (ii) given in…

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Q: 11T 60. Given that sec 12 13T V2 - V6, determine the value of sec 12

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

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Q: Consider the figure below. Assume that 41p,1, 1q, m263(5x+4)° m28 = (10x – 19)° a. Determine the…

A: straight line angle is 180 so ∠4 + ∠3 = 180°  if two lines are parallel then alternative interior…

Q: Calculate A and B so that t B %3D 1+1 (1-z²)

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Q: Express the following tunctrons in the form u+iv f(2)=In (I+z)

A: Solve the given problem.

Q: omplete his praol of Theoren 1. B Cive ZA and ZB with AĎ || BẺ; AČ || BĚ. F D Prove: ZA is…

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Q: If Z=1//2+j/v2 then the value * ?=of conjugate of Z^5

A: According to Euler, the complex number of the form cosθ+isinθ can be written as eiθ. The conjugate…

Q: 3 ) If f:(1,00)→ [2, 00) is given by F(x)=Dx+, find f(x), (assume bijection).

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Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension.

Q: Show that the functions x and x2 are orthogonal in P5 with inner product defined by (5), where xi =…

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Q: Find the source Q cx) Such that the So lutiim Uckit) of + Q(x) 2 ə x² 0 < x <∞ | U(x,o) = 0

A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

Q: c. Use De Moivre's theorem to find the following: 4 i. [1+ v3i]*

A: Dear learner, As per our guidelines, we can provide the solution for first one only. Kindly post…

Q: Find the angle between x and x4 in C[0,1] with its standard inner product.

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Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

Q: The curl of f(x,y,z)=xyzj is None of these. хуk-yzi О ху-yzk ООО О

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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: 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: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem