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

Q: 12. (a) 41 C NOT DRAWN TO SCALE In the diagram, O is the centrof the circle ABC and ZBCA= 41°. Find:…

A: We will solve both the parts of this question using only logic and some basic knowledge of geometry.

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…

A:

Q: If a bug walks on the sphere x + y? + z² + 2x – 4y – 2z – 30 = 0 how close and how far can it get…

A: Sphere

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. What surface in R3 is represented by the following equatic x = 7

A: In this question we will use basic of geometry i.e concept of plane. We will draw the plane on the…

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

A:

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

A:

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

A:

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…

A:

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

A:

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

A:

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

A:

Q: 글 36- +| de. 1 4 dz, (z+3i)³ ] Evaluate - z+3i where C is the circle |z+ 3i| = 6 + 4, 0 < 0 < 2ñ .

A:

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

A:

Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

A:

Q: Find the areas of the regions in Exercises : 1. Shared by the circles r = 2 cos 0 and r =2 sin 0

A: First find the common point or point of intersection of both the curves by equating both the…

Q: Find the areas of the regions in Exercises : 1. Shared by the circles r = 2 cos 0 and r = 2 sin 0

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: - Show that the area of the triangle whose vertices are the [x1 yi det X2 Y2 A - points (x₁, y₁),…

A:

Q: where C is the circle |z = 3i| =4. 2.3 Use the Cauchy integral formulae to evaluate 22 1 (9 – 22)(2…

A:

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

A:

Q: 2. Find the DE of all circles with center on thex - axis.

A:

Q: 2. Given: AB = AD; AACB and AACD are right triangles. Prove: AACB = AACD A B. D. 3. Given: KM 1 JL…

A:

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

A:

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: Find the areas of the regions . 1. Shared by the circle r = 2 and the cardioid r = 2(1 - cos u) 2.…

A: Hi! You have uploaded multiple questions. As per norms, we will be solving only the first question.…

Q: Prove or disprove that the point (1, V5) lies on the circle centered at the origin and containing…

A:

Q: The OT of the DE of the family of circles with center at the origin is (A) x= ky B xy= k x-y=k D)…

A:

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…

A:

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

A:

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

A:

Q: The OT of the DE of the family of circles with center at the origin is x= ky B xy= k x-y= k D none…

A: Solution

Q: 8- of What is the value of (z + e22) dz, where C is the positiv C oriented circle |z - 1= 1 in the…

A: Since z-1=1 ⇒z-12=1⇒z-1z-1¯=1⇒z-1z¯-1=1⇒zz¯-z¯-z=0⇒z¯z-1=z⇒z¯=zz-1

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

A:

Q: Use Green's Theorem to evaluate - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

A:

Q: In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. DB bisects…

A: Solution as follow

Q: z+i dz , where T is the circle Iz – 3i| = 1 traversed once (2) Compute counterclockwise.

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: 10. (~Ch16 Review #17) Use Green's Theorem to evaluate | x?y dx – xy? dy where Cis ,2 the circle x2…

A:

Q: 7. Use Green's Theorem (and no other method) to show that the area of the triangle with vertices…

A: Greens theorem

Q: 9. Determine the image of the circle z +- 2 P 1 2 3i under w(z) ==+l+i. Z

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: Let CR denote the upper half of the circle |2| = R for some R> 1. Show that eiz 1 22 + z+1 (R – 1)2…

A: ANSWER:-

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…

A:

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: Find the areas of the regions in Exercises: 1. Shared by the circles r= 2 cos 0 and r=2 sin 0

A: `1) Intersection   2 sin θ = 2 cos θ ⇒ sinθcosθ = 1 ⇒ tan θ = 1 ⇒ θ = π4   A = ∫ ∫A r d r d θ   A =…

Q: Find the areas of the regions in Exercises : 1. Shared by the circles r= 2 cos 0 and r= 2 sin 0

A: You have posted multiple questions. As per the instruction, we will be solving only one question. We…

Q: Find the area of the specified region. 3 and the cardioid A) (6r + 8) 9. в) - (5я - 8) Shared by the…

A:

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