Given, (2z – z) dz along the directed line segment from -i to 1. What is a parametric form of z(t)? 21- i(t-1) o+i(1-1) 1+i(1- ) 21 + i(t – 1)

Q: mplex function f(z) = z(z-21) have a removable

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Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: 2. (§1.1) Sketch the following set of points in the x-y plane. {(x, y) = R²: (y - x²) (y + x²) < 0}.

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Q: Find the general equation of the plane π  that passes through the origin and is perpendicular to the…

A: Suppose a plane passing through the points x1,y1,z1 and a vector perpendicular to the plane is…

Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

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Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

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Q: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

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Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: Let f(2) = Ln(2² + 1). Find a possible arrangement of the branch cut of f(2) on the complex plane.

A: Given: f(z)=Ln (z2+1)

Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: Find the Curl of the function f=(3x- 2y)k ?* O 2-3) O -2i+3) O 21-3) 2i+3)

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Prove that the point 2a +b-c, 5a -b+ 2c and 8a – 3b+5c are collinear.

A: Given, 3 vectors or points, A(2,1,-1) B(5,-1,2) C(8,-3,5)

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

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Q: Calculate / Ss (4xy + e- )dS, where S is the triangle in Figure 1 with vertices (0, 0, 3), (1,0, 2)…

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Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: - 3 - 2 Let y = u2 = Find the distance from y to the plane in R' spanned by u, and u2. - 6 u = - 5 1…

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Q: nt of intersectic -6 y + 8 = 3 O) カー

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