1. Use the expression z = r+ yi (not the polar form) to prove that |2| = |=l* for all z E C.

Q: [2.18] Derive an explicit form of the polar C* of the following cones: a. C= {(x),x2):0 x2 s2x1}. b.…

A: To find- Derive an explicit form of the polar C* of the following cones: C = x1, x2 : 0 ≤ x2 ≤ 2x1…

Q: 4. Consider the function w = cos z and the following two sets D = {z = x+ yi € C,0 1} i.e., R is…

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Q: QUESTION 8 Let A=Z and R ={(x,y)EA×A; x=y+1 or x=y – 1} Select the properties of R: Antisymmetric…

A: Relation

Q: C\[0,1] where C represent the complex numbers

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Q: 27 de Evaluate the intergal using the residue theorem. 15 +3 cos 0

A: residue theorem of integration

Q: determine where the given complex mapping is conformal. 3. f(z) = z + e + 1

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Q: Derive the canonical form of the given parabolic PDE (b) - 3u. +64.- 3u = cos(x).

A: given 2nd order PDE -3uxx+6uxv-3uyy=cosx   ...i claim- to derive the canonical form of given PDE

Q: 2.3 Use the Cauchy integral formulae to evaluate 22 – 1 (9 – 22)(z + 2i))3 where C is a circle |z +…

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Q: Determine the minimal polynomial for cos(π/3) + i sin(π/3) over Q.

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Q: Q : Let: z, 1-i and z2 = V3+i. Find z, 22 in the polar forn

A: Explained below...

Q: (c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)

A: Given: The coordinate transformation, x=Rsinhχsinθcosϕ y=Rsinhχsinθsinϕ z=Rcoshχcosθ The plane…

Q: Find the largest subset of the complex plane on which f(z) = cos(z)e-² is holomorphic, and the…

A: Given :  f(z) = cos(z¯) e-z¯ To find : We have to find the largest subset of complex plane on which…

Q: Let F = cos(5t) i+ 3tj+ 5t° k and G = ° cos(5t) i +²j+5e* k Find the cross product Fx G =

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Q: 3.2.14. Fix 1 <p< oo. Given x, y E lP, prove that ||r+ yllp = ||x||, + ||y||p if and only if x = 0…

A: Let x,y∈lp where 1&lt;p&lt;∞. Suppose x=0, then x+yp=0+yp=yp=0+yp=xp+yp Suppose y=αx, where α is a…

Q: Suppose N E L(C) is nilpotent and has a Jordan form with only one Jordan block. Describe a Jordan…

A: According to the given information,

Q: 29. Calculate /| (xy +e*)ds, where S is the triangle in Figure 18 with vertices (0,0, 3), (1,0, 2),…

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Q: 2.3 Use the Cauchy integral formulae to evaluate 22 - 1 Jo (9 – 2*)(2 + 2i))" where C is a circle |2…

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Q: 13R Q2 Put the complex number Z = 2e in the "Cartesian" form Z a+ bi where a, b E R.

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Q: 10. Given k = and n and m are positive integers. Prove the following orthogonality conditions: a) S,…

A: Given- Given k = 2πL and n and m are positive integers. To Prove- Prove the following orthogonality…

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: 1. Find the coordinates of the image of (-2, 4) under the following reflect (a) ay=o (reflection in…

A: Here we have to find the coordinate of the image of the (-2, 4) under the following reflections.  a)…

Q: for the Me quaton of the tagant bie kr the when al Curve

A: We use the definition of the equation of tangent line to the curve y= f(x), at point   (x0 , y0 ) to…

Q: 9. Prove (1, sin z, cos z} is linearly independent in [0, 2x].

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Q: Reduce to Canonical form Ur +5 ury +6 uyy = 0 %3D ミn= 0 3D0 =D0 None UgE =0

A: First option is correct.

Q: Let z1 = 2 – 3i , z2 = -1+ 5i , and z3 = -6- 2i. %3D 2123 Evaluate: z2 . Express final answer in…

A: The given complex numbers are z1=2-3i, z2=-1+5i and z3=-6-2i The addition  and subtraction of two…

Q: in C6. Evoluate the Rxpiession, write your ans wer polar and rectangulor form

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Q: السؤال 3 cos (z) =cosh (z) 0 صواب ihi O السؤال 4 The conjugate z of z=x+iy is z=x- iy صواب ihi O

A: 3. cos(z) = cosh (z) is FALSE

Q: 11 Find the coordinates of the image of J (8,7) after a reflection over the x-axis. AY 10 8 4 2 -10…

A: find the coordinates of the image of J8,7 after a reflection over the x-axis solution let a,b be the…

Q: 1. If z = x + iy is a complex number. (a) Verify that v2|z| > |Re(z)| + |Im(2)| [Hint: Reduce this…

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Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: -5 1 Let y = -2 U2 = = In 4 -1 Compute the distance d from y to the plane in R spanned by uj and u2.…

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Q: 3 If C is a circle of radius r with centre z, in the complex z-plane and if n is a non-zero integer…

A: Consider the given integral as, ∮dzz-z0n+1

Q: Given the states lp) = 3|0) – 2i|1) and |ø) = |0) + 5|1) , (a) Show that these states obey the…

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Q: determine where the given complex mapping is conformal. 4. f(z) = z + Ln z + 1

A: Solution..

Q: Evaluate the following and express the result in polar form. 1. In (1 +j2)* 5.47253.98°, principal…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Show that [0, o0) and [1, o0) are isometric.

A: We need to show that ,  [0 , ∞)  and  [1 , ∞) are isometric. We know that two metric spaces X and Y…

Q: Classify the following eq.,and reduceit to the canonical form: (1 (2) u -a²u (3)uxx +4 y = 0 = 0 (a…

A: The general linear second-order partial differential equation in the dependent variable u and…

Q: 1 Q2\ If z, = 2+ j, z, = -2+ j4 and Z3 1 evaluate z3 in the form Z, x +jy and in polar form.

A: GivenZ1=2+jZ2=-2+j4 The given expression is simplified as shown…

Q: , a curve in the z-plane and a complex mapping w = f(z) are given. In each case, find the image…

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Q: Find the decomposition of a(t) a = arT + aŋN into tangential and normal components for r(t) = (5t,…

A: Given rt=&lt;5t,2t2,2t3&gt; at t=1        rt=5ti+2t2j+2t3k       r't=5i+4tj+6t2k…

Q: 1 1 1 Q2\ If Z = 2+j, Z, =-2+ j4 and Z3 evaluate z, in the form %3D Z, z, X +jy and in polar form.

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Q: Consider the following PDE Uxx + 2x uxy + Uy = 0 a) What is the class of the equation? b) Reduce the…

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Q: 1234 5678 9 10 11 12 13 14 Find the coordinates of the image J (8, 7) after a reflection over the…

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Q: Let F: IR3 →IR3 is a diffeomorphism and M is a surface in IR3 , prove that the image F(M) is also a…

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Q: What is the polar form of (2+ j3) x (4- j5)? O 23.09/31.3° 23.09/5.0° O 19.2545.0° O 19.25Z31.3°

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Q: a) Show that u(x,y) = x3 – 3xy2 + 3x2 – 3y2 is harmonic and find its harmonic conjugate

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Q: 5. Describe the counterclockwise rotation that maps AQRS to AQ' R' S'. 8 4 -8 -4 O 4 S'8 -4 R' Q' CO

A: Given a graph of transformation of triangle

Q: Let φ1 = 1, φ2 = x, φ3 = x2 on the interval 0 ≤x ≤1. Find the following inner products: (a) (b)…

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Q: Find the curl of = pz²cos(p)a+zsin²(p)a₂ O None of the choices O2zsin (4)…

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