4 3 Compute o dzwhere C is the circle 2- i = 2 traversed once z+2i (2- 2i), C. counterclockwise Select one: None of these ST NEXT PAGE

Q: 3. a) Compute : S, (Re z – 3z) dz where r is a directed line segment from z = 0 to z = i . b) Let C…

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Q: 8 If C is a circle of radius r with centre z,, in the complex z-plane and if n is a non-zero…

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Q: 5.1 Find the upper bound of ez?+1 zp- (z – 1)2 + 5 where C is the circle |z – 1 = 2.

A: We have to find the upper bound of ∫ez2+1z-12+5dz over the circle C such  that z-1=2. Observe that…

Q: 1 Evaluate 2 4 |dz , (z+ 5i) 3 niPc54 + Z+ 5i where C is the circle |z + 5i| = 4 + 2, 0 s 0 < 2n .…

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Q: 3. a) Compute : S, (Re z – 3z) dz where r is a directed line segment from z = 0 to z= i . b) Let C…

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Q: 13.10. Let y be the circle |z| = 2. Show that 1 dz- z2 – 1 3

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Q: 4. Describe the reflection(s) that will carry the rectangle onto itself. 10 -10-9 -7 01 -2 -6

A: Given: The rectangle ABCD. To describe: The reflection of rectangle.

Q: By Green's theorem, if C is the circle x2 + y? = 4 taken anticlockwise, then fv dz - z'dy, equals…

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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: Let S be a circle with its center at point O and a radius of 1. Let AABC be a triangle such that all…

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Q: 1. E is a triangle with vertices (1,0,0), (0, 3,0) and (0, 0, 2), with 8(x, y, z)=xz+1.

A: Note: As per our guidelines we are supposed to answer only one question and the rest can be…

Q: In the figure, ABCD is a cyclic quadrilateral. AB // DC in circle with centre O. BC and AD produced…

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Q: 1 Evaluate 4 7 27 + z + 2i dz, (z + 2i) 3 C where c is the circle |z + 2i| = 7 + 4, 0 s 0 < 2n. %3D

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Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

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Q: 2. Let O = (0,0) be the origin and consider the inversion Io,5- (a) Compute Io,5(-2, 3) and…

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Q: 4. Consider the following diagram. 8т — 2n | 13 2m + n 4m + 1 Find the values of m and n that prove…

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Q: 1: One of the hayfields on Rob's farm has shape and size modeled by a quadrilateral QC R? with…

A: Given:- Corners of the quadrilateral hayfields farm  is (3, 1), (6, 2),(3, 6) and (2, 4) We first…

Q: In the diagram, O is the centre of the circle and A, B and D are points on the circle. Use Euclidean…

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Q: 6. Given a rule x² + y? = 9, its image rule x² + y² – 2x + 6y + 1 = 0 under a translation, state a…

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Q: The triangles T_1 defined by (0,0), (1,1). (3,0) and T_2 defined by (0,-1), (-1,-2), and (0,-3) are…

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Q: 4. If AB is a diameter of a circle with center P, and X ånd Y are polits UI circle such that XY…

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Q: By Green's theorem, if C is the circle r + y = 4 taken anticlockwise, then z*dy, equals -27. none of…

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Q: 2.2 Find upper bound of 2+4 (z – 3i)³ + 1 where C is the circle |z – 3i| = 4.

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Q: 1 Find the upper bound of (z-1)2 +5 where C is the circle |z – 1| - 2.

A: As per the guidelines, as there are multiple questions, first question is to be answered. Kindly…

Q: 5.1 Find the upper bound of (z – 1)? + 5 where C is the circle |z – 1| = 2.

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Q: 1) Prove that AABC = ADCB: 3) Prove that AABD ACBE: A B. 卡 E C A 4) Prove that AMBE = AMCD: 2) Given…

A: If two side are equal and one angle then by SAS rule triangle are similar

Q: O -L -5) O4-

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Q: 1.1 If C is circle |z – 2i| = 2, then Sc [ + (z – 2i)²] dz А. 0, B. T, С. 5л, D. 10ri, E. None of…

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Q: 6 Consider the circle K = {z EC: |z| = 3} and n points a1, ..., an EK (n > 1). Show that there…

A: Consider the circle K=z∈ℂ: z=3. Let a1, a2,…,an∈K be n≥1 points. Consider the function f:z∈ℂ: z≤3→ℂ…

Q: 9. What is the resulting image of D' after a reflection about the line y3Dx? ty D Rule: A B

A: Topic - symmetry and geometry

Q: 3. Let C be the positively oriented circle |2| = 2. Compute the following integral: 726+글 exp(를)…

A: We have to find complex integral using Cauchy Gaurast Theorem. Cauchy-Goursat Theorem. If a function…

Q: 23 +3 Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7. 22…

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Q: 5. If z is any point on the circle |z1 – 2| = 2, then prove that - 2 arg(z – 2) = 2 arg z = arg (z²…

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Q: b) Let C be the circle |z| = 4 traversed once in the positive sense (counter clockwise). Compute : P…

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Q: 4. 3. B. drawn. Prove by congruent right triangles that BB' = AO and AQ = CC'. What conclusion can…

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Q: 1. Sketch the path C which is around the paths one from z = 3i to z = 2i and another from z = 2i to…

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Q: 2 10 급fe| 310 dwhere C is the circle |z+ 3i| = 10 + 2, 0 < 0< 2n Evaluate z+3i (z+3i)

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Q: I, 7y? da, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

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Q: 2.2 Prove that ne dz < 3 e 2 ++1 whore C is the arc of the circle 2| = 3 from z = 3i to z = -3. %3D

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Q: 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: Introduction : Given a circle C with radius r and center z0. Then we have asked to calculate the…

Q: 1. [7.5] Using Cauchy Residue Theorem, evaluate 2z+ 22 + where the contour C is the circle |z – i| =…

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Q: 8. Use the diagram of circle H to find JK if DG = 24 and FH=I %3D G. JK = D 7, F.

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Q: Use Green's Theorem to evaluate §+(x² - y²)ẩx + xảy, where C is the circle x² + y² = 9. Select one:…

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Q: II Let S be a circle with its center at point O and a radius of 1. Let AABC be a triangle such that…

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Q: B) Evaluate fLn z dz around the circle | z| = 2

A: Ln z has singularity at z = 0. But we cannot use residue theorem as Ln z has non isolated…

Q: 12. What is the resulting image of L' after a reflection about the y-axis? Rule: K IN

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Q: 2.2 Find upper bound of zp (z- 3i)3 + 1 where C is the circle |z - 3i = 4. 2.3 Use the Cauchy…

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Q: a. Let z1 = 2 – 3i, z2 = 3 + 4i and z3 = 1– V3i. Find z1z2 + z3 then sketch it on Argand diagram.

A: Simplify Z1Z2 + Z3 in simplest form and convert it into polar co-ordinates.

Q: 2. If one of the vertices of the square circumscribing the circle|z – 1| = /2 is 2 + V3i. Find the…

A: Solution

Q: 3.1 Show that upper bound of fe dz, where C is the circle |z + 4 – il = 7. z+5i-1

A: The given problem is to find the upper bound of the given complex integral over the region of circle

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: