i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

Q: M=N

A: answer is in next step

Q: -z Q2. In the circle |z| = 1, Find the upper bound for 9z4+3z²+2l

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Q: COSTZ (iii) dz, where C is the Jc (z²-1)2 circle |z – 2| = 2 counterclockwise.

A: Let fz=cosπzz2-12 and C is the circle z-2=2 fz can be written as fz=cosπzz2-12=cosπzz-12z+12…

Q: Let C be a positively oriented unit circle. Compute the residue of the following: (a) f(z) = z(z²+4)…

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Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: X. Let C = C₁ UC₂U C3, where C₁ is the line segment from (-1,-1) to (0,0), C₂ is the line segment…

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Q: 2+2 c(z+1)²(z²+1)' 3. Determine dz, C: CCW rectangle with vertices (+2,+2), (±2,F 2).

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Q: The real part of (11x + 1 + iy)dz where C is the line joining 1- i to 2+ i is Answer:

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Q: 4. Let C be the circle |z| = 3 traversed once in the positive sense 2z-17 (counter clockwise).…

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Q: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: Show that 25+ 2z² + 3z + 2 has five zeroes inside the circle |z| = 2, and determine the number of…

A: If f(z) and g(z) are two analytic functions within and on a simple closed curve C such that |f(z)|…

Q: 3. Perform the following operations and find the degree of the result a. (2r- 4x² +7)+(3.x² – 12x-7)…

A: According to guidelines, first three subparts are to be solved. Please repost the remaining.…

Q: Consider the shaded region shown in the figure that involves the curves of equations: (x - 1)2 = −4…

A: We have, two curves: x-12=-4y-1 and 9x2+16y-22=144 To find the area of the region  First we will…

Q: Sc₂²2²4 dz, z-7 z²+z-2 where C is the positively oriented circle of radius 4 centered at z = 0.…

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Q: - - Find the cross product (-2i - j + k) × (3i − j − k). Answer:

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Q: Prove the midpoint formula by using the following procedure:a. Show that the distance between (x1,…

A: We have to show that, the midpoint formula by using the following procedure: (a) Show that the…

Q: 1 € /₁ (2² + 1)2 dz. Let C be the circle |zi| = 1. Evaluate

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Q: Calculate [(ydx – xdy)] wherein y(t) = (2cos(t), 2sin(t)),0 < t < - 27, is an circumference that…

A: Integration

Q: Calculate the following integral 1 Lc (z − 1) (2³ — 1) dz for each of the following contours C. In…

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Q: Verify that the circles x² +y? – 4x – 7y +6 = 0 x² +y? + 3x – 14y – 1 = 0 and, 3(x2 + y?) + 2x – 35y…

A: Given:   Let S1=x2+y2-4x-7y+6=0         S2=x2+y2+3x-14y-1=0         S3=3x2+y2+2x-35y+4=0    Now,the…

Q: Using the Residue Theorem, or otherwise, compute z-7 z²+z-2 dz, where C is the positively oriented…

A: Let  fz = z-7z2+z-2           Consider  z2 + z - 2 = 0…

Q: Given that F = (2x + y2)i + (3y – 4x)j. Verify Green's theorem for F.dr around the triangle formed…

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Q: Find the distance between G(-4, 3) and H(4, 7). Show all of your work. d = √√√(x₂-x₁)²+(y₂-y₁)²

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Q: What is the distance between the given pla P₁: z=x+2y + 1 P2: 3x + 6y-3z = 4 O 0.95 O 1.50 O 0.14

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Q: Segemnt JK has endpoints J(a,2b) ans K(3a,4b) Find the midpoint.

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Q: Find the trace of the plane 4x - 12y + 7z = -9 in the coordinate xz-plane. (Use symbolic notation…

A: Equation of plane .To Find:Trace in xz plane.

Q: Use the Midpoint Rule with m = n = 2 to estimate the value for R= [0, 4] × [0, 6]. √ √ ( 3x + 2y) dA…

A: Sol:- To use the midpoint rule with m=n=2, we need to divide the rectangle R into 4 smaller…

Q: 1 Let f (z) = . Let C be the circle |2| = 2n the counter-clockwise direction. What is 2ri Lf(2) dz?…

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Q: z-72+3 Using Cauchy's Integral Formula Evaluate where c is the circle lIzl = 2. z+i

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Q: m while the (2) Find the ualue of the constanl Curl of Fasie) = mxy.ge?) Ĉ + cm-7)xi+ (I-m)×2°R is…

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Q: Using the Residue Theorem, or otherwise, compute z-7 Sezzzzzz dz, z²+z-2 where C is the positively…

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Q: + 4z 53. Use (7.8) to evaluate dz around the circle |z – 2i| = 2. - z4 + 8z2 + 16

A: Given,  ∮z3+4zz4+8z2+16 dz  around the circle z-2i=2

Q: j √(6y 7 + 9z 7 + 6xk) · d7 where C is the boundary of the triangle with vertices (3, 0, 0), (0, 5,…

A: First parametrize the boundaries of the triangle. (3,0,0) to…

Q: i fc 78 8 Evaluate dz, where C is the circle |z+ 7i| = 8+6, 0<0< 27 z+7i (z+78)"

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

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Q: Using the Residue Theorem, or otherwise, compute 2-7 +z-2 dz, where C is the positively oriented…

A: Let  fz = z-7z2+z-2                consider  z2+z-2 = 0…