The scalar product equal (with philand phi 2 is orthonormal) lw> =i\@,> -2|@,> Ix> =3|0,>-2i|92>

Q: sing the relation z=x+iy = rcosθ + irsinθ=re^iθ . Derive z^n = r^n(cosθ + isinθ)^n = r^n(cosnθ +…

A: The relation .The aim is to derive the expression .

Q: 3. Find the complex Fourier Series for periodic extension of: x(t) = sin(2t) %D for 0 <t< 2T

A: Note: Since you have posted multiple questions, according to the policy we are only allowed to solve…

Q: Explain fermat's little theorem.

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Q: Z=5-2(i^1/2) Find modul [z] Arg [z]

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Q: Solve if w be cube root of unity then (1+w)(1+w^2)(1+w^4)(1+w^8).....2nfactor=1

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Q: Find the integrals using complex analysis x' +1

A: "Hey, thanks for the question. Since there are multiple questions posted, we will solve the first…

Q: f(x) = [sin x if 0 T

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Q: a) f(z) = vz+Vz - 1 b) f(z) = Vz2 +9 %3D

A: A branch point of an analytic function is a point in the complex plane whose complex argument can be…

Q: (a) A = [í 21 B = R s c= D= -2 -5. 4 = G ) B= = L, ) = 5[ -3 -5 (b) A = [; ) B =[ D = 5 -11. -5]

A: Givena)A=2112, B=-30-2-5 , C=-2-402, D=0000.b)A=1114, B=-3-50-11 ,C=19-110 , D=-55-20-25To find All…

Q: ZA'B'C' is the image of LABC following the reflec- tion of ZABC across line (. If mZA'B'C'= + 20 and…

A: Given: m∠A'B'C'=x5+20, m∠ABC=x2+5 We know that when we take reflection of a triangle across any line…

Q: State Fermat’s Theorem

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Q: Let flox) - I=39 1-3x %3D

A: Answer and explanation is given below

Q: PC=2х7-5x6+4x4-3*3+2*-4

A: We can use the intermediate value theorem and the fact that polynomials are continuous functions to…

Q: Solve each of the equations for x in the interv [0,2pi) A. Csc^4x-3csc^2x+2=0 B. Radical…

A: We have to solve the following equations for x in the interval 0,2π. A. csc4x-3csc2x+2=0B.…

Q: [2 4 21 A = l1 3 1 1 1 B = -2 -1 [2 4 D = 4 C = 1 3 21 -1 %3D 2

A: Given A = 242131B = -1111-2-1C = 242131D = 1-1-1-121 Clearly  C = AD = -B

Q: Find all zeros of the function. (1-cosz)( z^2+1)(z^2+1) Give the order of each zero.

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Q: Distance between (9x,-11x)and(4x,x)

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

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Q: Let Z = 3 + 5i and let W = 3e^(3ipi/4), find ZW, Z/W and Z + W using de Moivre's Theorem

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Q: Express (-2/3 + j2) in rectangular form.

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Q: Let F be the vector field F(x,y, z) yzi + xzj + xyk and C the ellipse given by r(t) = 5 cos t i+…

A: Given vector field: Fx,y,z=yz i+xz j+xy k The ellipse C is given by: rt=5costi+3+2sintj…

Q: Z = x +yi. How do i describe (Z/(Z+1)) into x + yi form?

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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line…

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