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- 5z +3 Find the domian of not analyticity of f(z)= sinh z - i (T + 2kn)i TT 2+ + 2kx)i + 2kn)i 2. 2+ (7 + 2kr)i1. help pls1. Find curl(v) of the following in terms of (x1, x2, x3) and (e1, e2, e3). If curl(v) = 0, find the function f such that Vf = v. a. v(x) = (x² + x + x3)-'(x1e1 + x2€2 + X3@3). b. v(x) = (xỉ + X2X3)e1 + (x3 + X1X3)e2 + (xž + x2X1)e3 c. v(x) = e"1(sin(x2) cos(x3)e1 + sin(x2) sin(x3)e2 + cos(x2)e3)
- 1.2 If R₁ = 2i-j+k, R₂ = i +3j - 2k, R3 = -2i+j3k and R4 = 3i+2j+5k. Determine scalars x, y, and z such that R4 = xR₁ +yR₂ + zR3.5B Given the inner product space of polynomials with real coefficients, degreeThe quadratic form is positive-semidefinite but not positive definite negative-semidefinite but not negative definite indefinite qA (x, y) = x² + 2xy + 3y² negative definite positive definiteConsider the following quadratic form on R²: 43 2 57 2 + -x7² 25 -X₂ 2 25 Q(x) = [₁] = 48 a) Determine whether Q is positive or negative (semi)definite. b) Find a change of variables x = Py that converts Q to a form with no cross-product terms. c) write Q in terms of the new variables y 1 and y2. In your formula, write 'y_1' and 'y_2' for y₁ and y2. Use the square root symbol 'V' where needed to give an exact value for your answer. [00₁] 0 0 1 00 42 +. a) The quadratic form is c) Q(x) = 0 25 -X1X2 Positive Definite Negative Definite Positive Semidefinite Negative Semidefinite Indefinitei) Find all values of z such that 25 = -1+ v3i. Plot your solutions on a complex plane. ii) For a complex function f(2) = u(x, y) + iv(x, y) with u and v real, the Cauchy-Riemann conditions state that f(2) is analytic if and only if dv du and ду du dx dy Let fi(2) and f2(2) be two analytic functions: prove that the function g(2) defined by g(2) = fi(2)f2(2) is also an analytic function. iii) Using the result of part (ii), or otherwise, determine whether the function f(z) = ze is analytic.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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