-dz where C is the circle |z|=3. (z+ 2)* Evaluate

Q: : If F=(x2+y2 )i - 2xyj +xk, evaluate ∫ ?. ?? c if the contour is that portion of the circle x2 + y2…

A: F=x2+y2i-2xyj+xkTo evaluate ∫CF  da if C is given by x2+y2=a2 from the point (a,0,3) to(-a,0,3).

Q: Evaluate | dz where c is the circle z| = 2. z (z+4)

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Q: dz where I is the circle z =1 traversed in the counter is 0 0 2ni o 2n O, -2ni

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Q: Let f (z) = SLet C'be the circle |z| = 2in the counter-clockwise direction. What is | f(2) dz 2ri C

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Q: Find the curvature k of the circle C : (x – 2)² + (y + 3)² - at the point (5, 1).

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Q: (c) Evaluate L A – 423 + 4z² dz where C is the circle |z – 2| = 1. , z4 – 4z3

A: Given,       ∮C4z+2z4-4z3+4z2dzwhere C is the circle z-2=1

Q: e iz dz where C is the circle z =3. zーT/2 Find,

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Q: cos TTZ 6. Evaluate -dz, where C is the circle |z| = 4 c 23-7z+6 ezt

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Q: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

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Q: z dz 2z ² +(1+i )z -i C is the circle |=|=2

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Q: dz Find an upper bound for 9c z4 –5z²+6 dz, where c is the circle |z| = 4.

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Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

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Q: Evaluate F dī , where F(x, y) = (e* +x² )î +(e' – xy²)ĵ and C is the circle x² + y2 = 25, oriented…

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Q: O Evaluate + z )ds where C is the circle F(E) = for 0EEE Zo

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Q: -dz Q5/ (A) Find the value of the integral 3 where C is the circle z+2 = z(z+1)"*1

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Q: e2z dz, I (z+ 1)* (b) Where C is a circle |z| = 3

A: The given integration is ∮ce2zz+14dz where c is the circle z=3 Here the pole z=-1,which is of order…

Q: dz where T is the circle z=1 traversed in the counter is 0 0 2πί ο 2n O; -2ni 10 Jlgull ezt dz

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Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

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Q: Let f (2) = 5. Let C be the circle |z| = 2 in the counter-clockwise direction. What is 2ni Tf(2) dz?

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Q: Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval [-1, 1].

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Q2) Find the distance between the line y= - (x+2) & the center of the circle y+x-4(x+ y)= 9

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Q: zt e dz if t>0 and C is the circle z]=2. Evaluate 2ni C 2πίz+1

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Q: (y - eCos(e25! dx + (x2 + y+1) dy, where C is the circle r = 2.

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Q: Find the curvature k of the circle C:(x – 2)2 + (y +3) = 25 - at the point (5, 1).

A: circle equation is x-22+y+32=25 and point 5,1find curvature k

Q: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

A: We will find out the required value.

Q: Compute . Z+1 dz, where C1 is a part of a circle with r = 3, and 0<0< %3D

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Q: 3. If y = 7x cuts the circle x² + y² = 50 at A and B. Find the coordinates of A and B. %3D %3D

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Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

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Q: b) |Im(z)dz, where C is the circle |2| = 2 traversed once counterclockwise. %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine the area of the region in the second quadrant that lies between the circle r = π and the…

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Q: Let f (z) -Let C'be the circle z 10in the counter-clockwise direction. What is 1 -Lf(2) dz? 2ri

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Q: 2z-3 3. Jc 3-372+4 dz, where C is the circle |z| = %3D counterclockwise.

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Q: z+2 Evaluate. z2-5z+6' where c is the circle |z| = 2.

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Q: ㅠ Use Green's theorem to find: where C is the circle x² + y² = 4 going counter-clockwise. -8T […

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Q: Find the image of the circle /z/ 4 under f(z) = Lnz %3D 5-(15pts) Evaluate S-3/2

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Q: Evaluate xy ds, where C is the right half of circle x² + y² = 4 and is traversed in the clockwise…

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Q: dz b) C: z|= 4 is a circle calculate the integral .(z-1)(z² +9)

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Q: Find the curvature K of the circle C: (x - 2) + (y+3)² = 16 %3D at the point (2, 1).

A: Given: Equation of circle C: (x-2)2+(y+3)2=16 ⇒ (x-2)2+(y-(-3))2=42 We know that circle equation is…

Q: Q2) Find the distance between the line y= - (x+2) & the center of the circle y+x-4(x+ y)= 9…

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Q: Q5. Prove that the circle {(r, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1].

A: Here we can prove this question using topological property connectedness.

Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

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Q: 2z Evaluate] (7-1)(z-2) dz where C is the circle z=3

A: See the attachment

Q: e iz -dz where C is the circle z =3. z – 1/2 Find, /2 - 2T - 2z - 2

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

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Q: Vhat is the equation of a circle with center (3, –7) that goes through the oint (1, 1)? D (x – 3)2 +…

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Q: Q4: Evaluate fo z² - 3z + 1 z + 2i -dz 312 where C is the circle |z + 11 = ²/

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