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 dz then o equals (7 - z. in+1

Q: 2. A circle of center O and radius 180 intersects a circle of at Q. Prove that AP- AQ = 172 if and…

A: Topic- simplification

Q: 10. Since fis holomorphic everywhere except at z = -lit is known that it maps infinitesimal circles…

A: Given fz=z-1z+1. Then f is holomorphic everywhere except -1. Let z=-1+14i. Then,…

Q: 3. (a) Suppose AABC is a triangle on the unit sphere S and suppose A = π/4, B = π/3, and C= π/2.…

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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: 7) At the right is the top view of a Chemistry Butiding in UP Diliman. It resembles the famous…

A: The sum of a polygon's internal angles: The following formula is used to determine the sum of…

Q: 5.If A. B,and M are three collinear points,such that M clevides AB internally in the ratio 3:4 and a…

A: section formula for internal division  in vector form is OP→=nOP→+mOP→n+m According to the question,…

Q: Let z be a complex mumber o B19) s and c be any then So BlE)dz+a fle) dz isequi contou any funckon…

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Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: 9. Find the area of the trapezold 12 in. Circle One: 45-45-90 -30 in. 30-60-90 SOH-CAH-TOA…

A: Explained below

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: 3(2x + 1) = 5(x - 4) BOTH SIDES on both sides In the umn, circle the equotion to sh 1 5+ (6x + 9)…

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Q: 1.) a) Find the roots of the equation z' +(1+ \3i) = 2z+1 b) Sketch the set Im <1 and determine…

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

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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: 1. Let points A, B, C be located as shown in Figs. 4.11 and 4.12. Construct the harmonic conjugate…

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Q: Sketch z =- 2cos y in R3

A: The expression y=cos(x) will give the graph of a cosine curve in the x-y plane, with the value of y…

Q: 1) Prove that A is uniform pentagon and B is a half of a circle, also determine the areas of A & B.…

A: Here I am attaching image so that you understand each and every step. solutiongiven data (Let…

Q: 2. Let K be a finite simplicial complex and n is equal to the number of path-connected components of…

A: For simplicity, here we use r, instead of n.

Q: By sketching the appropriate loci on an Argand diagram, find the value of z that satisfies |z|=13…

A: For the solution follow the next step.

Q: 5. In AABC let the bisector of ZB meet the circle containing A, B, C in a point E distinct from B.…

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Q: A set S is said to be convex if each pair of points P and Q in S can be joined by a line segment PQ…

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Q: 3. Given the complex mmbers z, = 4+3i z, =2-4i , find a) z,22 c) z,°z,

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Q: State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for…

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Q: Find the equation of the line through P = (4, 12) such that the triangle bounded by this line and…

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Q: 3. Find the constants bo, co, a1, b1, C₁ so that So(x)=1+ box + cox² + x³, S(x) = { S₁(x) = a₁ - 2x…

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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: (a) A rectangle has area of 96 ft2 and perimeter of 40 ft. Find its dimensions. (b) Prove the…

A: 5.  (a) Given that the area of the rectangle is 96 ft2 and the perimeter is 40 ft. Let x be the…

Q: Prove that z'e'-z = 1 has exactly two roots inside the circle |z] = 1.

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Q: 4 3 Compute o dzwhere C is the circle 2- i = 2 traversed once z+2i (2- 2i), C. counterclockwise…

A: By cauchy integral formula we can solved the problem

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: 1. Let a, b, c E R, and w' = 1, with w # 1 has strictly positive imaginary part. If a, b, c are not…

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Q: Based on the results of a test for symmetry, which of the following equations demonstrate e =…

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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: Find the Zero and its order for the funcation fcz) = 1 -Pit z te.

A: We know that, f(z) = (z-z0)n has zero of order n at z=z0, if f(z0)= 0

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: 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: ABCDEF is a regular hexagon with centre O. OA = a,OB = b and M is the midpoint of BC. X is the point…

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Q: The points A, B, C and O represent the numbers z, =, 1 and 0 respectively in the complex plane.…

A: We will treat A,B,C as position vectors to do the proof

Q: A headlight is being constructed in the shape of a paraboloid with depth 3.5 inches and diameter 8…

A: Solution is given below:

Q: Select all the Points through which a unique solution for the DE ,2 y? IS nySot eed by the Existence…

A: Given differential equation is y'=13-x2-y2

Q: What are the perpendicular generators on (P) to 4 %3D of the surface

A: Given equation s are, x216-y24=z....1x3=y2=z-4...2 Equation of generators of the hyperboloid (1) are…

Q: 12 In the diagram below, GI is parallel to NT. and IN intersects GT at A. A G Prove: AGIA~ ATNA

A: Consider the given triangles, In this diagram GI∥NT and IN intersects GT in A.

Q: 1. (a) Let 5 -6 -6 B = |-1 4 2 3 -6 -4 Find oigon nigon un imil to D

A: To finding the eigenvalues and eigenvectors to the given matrix we use Gaussian elimination method.…

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: A natural cubic spline is defined by [a, (x – 1)' + b, (x – 1)² +c, (x – 1) + d, f(x) = if 0<x<1 (x…

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Q: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem

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