Z, = 8 + i Find z of z, using Moivre's formula

Q: A- Find all values of z such that sinh(z) = e'ő. B- Are |z], Img(z) analytic? Give reason.

A: Solution of the problem as follows

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Q: zl 5. Trigonometric form of the quotient of = 6cis (2); z2 = 2cis () is:

A: The given quotient of z1=6cis2π3; z2=2cisπ6. Find the value in trigonometric form.

Q: a) Find the area of the reason that lies inside the circle r= 3a cos 0 and outside the cardioid r=…

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Q: Find the product z;z2 and the quotient 1. Express your answers in polar form. z2 cos()- + i sin), z2…

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Q: 5. Let C be the unit square with diagonal corners at –1- i and 1+i. Evaluate O f(z) dz, where f(z)…

A: Cauchy Integral theorem states that if fz is analytic in a simply connected region D then for any…

Q: an´e+ cot´e+2 = sec'e cosecʻe Prove the following identities

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Q: . r= 2a cos e %3D

A: We have to find the area enclosed by the given polar curve: r=2acosθ ; 0≤θ≤2π

Q: Find the area of the region shared by the cardioids r= 12(1+ cos 0) and r= 12(1- cos 0). The area…

A: General equation of the cardioids is r=a(1+cosθ) and Area of the cardioids is 6πa2

Q: Consider the polar form z = 2 cos + i sin 2' 10, What is the modulus of z10? 10 What is the argument…

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Q: Prove that the Lagrange's formula can be put in the fom ø (x) f (x,) n P „(x) = Ë Σ %3| r= 1 (x- x,)…

A: The Lagrange's formula is…

Q: + 151 of 305 → B Glven: Cis the midpoint of AE. Cis the midpoint of BD. AE = BD Prove: AC 열 CD…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: 2. Solve for z. Assume no full rotation. 23 = 2 + 2i O z = e% O z = V2e'i O z = 2ei O z = 4e*i

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Q: iv) z, = ei01 ,Z2 = el62 then z,. z, = ei(81-02)

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Q: 11.5.11 Find the area shared by the circle r, = 4 and the cardioid r, = 4(1 – cos 0). %3D The area…

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Q: O1: Using Bisection Method, find the Root of the following equation: , for the interval (0,1) Cos x…

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Q: ST,¥. xキマ 1. Verify C ノyジ * =ンycO

A: Since, we are asked to solve using Stokes theorem only, we will use theorem to evaluate the integral…

Q: 4. Find the distinct roots of z for the following equation, z4 = 3i. %3D 5. Prove by taking z = a +…

A: Q4) Given that z4=3i So z4=3iz4=3cosπ2+isinπ2z4=3cos2nπ+π2+isin2nπ+π2         Since sin and cos are…

Q: 61. The area of a triangle is to be computed from the formula A sab sin 0, where a and b are the…

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Q: Develop a quadratic equation in x for the data point depicted as follows: (1,10), (4, 13), and…

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Q: Skatchhograph f(x) 12X-12 OK X <Z of the fonctien and locate the absolute extrema on the Interial…

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Q: #20. USE TRIGONOMETRIC FORMS TO FIND z1/z2 а. z1 = -1 + i, Z2 = 1 + i 2, i b. z, = V3 – i, z2 = - V3…

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Q: de Evaluate the intergal using the residue theorem. 13 +4 sin e

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Q: Let I = x cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is: O…

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Q: əz Use chain rule to find at where z = e2" sin (30) and r = st – t², 0 = Vs² + t². %3D

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Q: u(x,у)- (sin x)(e' — е").

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Q: nd the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form…

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Q: (a) Given r(t) = 't+1' cos t , , e'), find the Domain of r(t) and lim, r(t). %3D t-n/2

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: = S,x2cos (x) dx. The approximation of I using the two-point Gaussian quadrature formula is: O…

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Q: QUESTION I 11 the figure below, acute-angled AMBC is drawa having C at the origin L11 Prove that c…

A: Explanation of the answer is as follows

Q: Q1- Consider AB in Figure as part of an electric circuit. Find H at the origin due to AB. 6 A

A: By using Biot-savart Law's  Madnetic field at point 'p'

Q: Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use…

A: Given: z5 = 3-2iz   = 3-2i15                                     1-------------------De-Moivre's…

Q: Q: Use Lagrange's Formula to Prove that :

A: Solution: We know that Lagrange's interpolation formula for unequal intervals is, f x =  x-x1  x-x2…

Q: Let / L sin(x +1) dr. The approximation of I using the two-point Gaussian quadrature formula is: O…

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Q: Interpolate the value of the f(2,1) using Lagrange's interpolation formula with the following set of…

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Q: Let I = x? tan(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 3. Find the length of the curve r = a (1 - cos 6) from 0 = 0° to 0 = n and also the total length of…

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Q: Evaluate (counterclockwise). (Show the details) tan(πz) 24 -dz, C:²|2+1²=1

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Q: a b Let A = and let k be a scalar. Find a formula that relates det(kA) to k and det(A) c d

A: Given that, A=abcdk is a scalar

Q: Find all values of A E C such that A(1+2i, 5+4i) = (3+2i, 6-1)

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Q: Let R := Z5[i] . a. Is 2 + 3i a unit in R? b. Find the idempotents of R. c. Find the characteristic…

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Q: Let I = ,x² sin(x + 1) dx. The approximation of I using the two-point Gaussian quadrature formula…

A: Fourth option is correct

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: Let I = x² sin(x) dx. The approximation of I using the two-point Gaussian quadrature formula is: O…

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Q: Let I = x°cos (x) dx. The approximation of I using the two-point Gaussian quadrature formula is:…

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Q: using finite Fourier tran form, solve du given ulo,t) =0, U(4,) =0 and u(x, 0) = 2% -2X where o<x…

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