dz Evaluate the integral o - 5i' C the circle |z| = 47 counterclockwise. NOTE: Enter the exact answer. dz 5i Does Cauchy's theorem apply to this problem? Choose onei

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

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Q: Let f (z) = 470 = Q A = 2and B= 2 + 2Let C1 be the contour composed of the line segments O Aand AB…

A: Let x(t) and y(t) be two real valued continuous function an[a, b] then z(t)=x(t)+iy(t), t∈[a,b] is…

Q: (ii) (iii) dz c (z²+4)³ where C is the circle |z-i=2 (z-1)dz (z+1)²(z-2)' 1- where C is the circle…

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Q: QUESTION 6 Use the Green's Theorem to evaluate the line integral xfydx +xy dy. where C is the…

A: Using the given vertices we can draw the required triangle and then apply Green's theorem to…

Q: Ex(6):-(H.W) Find the center and the radius of the circle whose eq x'+ y' +x+3y 7

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Q: z?-7z+3 Q:5 Using Cauchy's Integral Formula Evaluate f z+i „where c is the circle Iz| = 2.

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Q: Compute the line integral -xdy + ydx 2(x-y)2 +4xy where L is the circle (1-x)2 + y2 = 3 with a…

A: We can write the given line integral as ∫L y2x-y2+4xydx+-x2x-y2+4xydy, where L is the circle…

Q: where C is the circle with positive orientation. e2021z dz Yo (22 + 4)² (2² – 1) (a) C: |2 – 2 – i|…

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Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

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Q: solve for no. 4 and 5

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

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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: dz where C is cir

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Q: Let F (x, y) = 8Q A. Compute 82 yi+zj z² + y² and let C be the circle r(t) = (cost)i + (sin t) j. 0…

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Q: o F. ds, where F(x, y) = x²i+x²j and C consists of the arcs y = x² and y = x for 0 < x< 1.

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Q: Under the transformation w = :-1 -find the image of the circle E = 1 in the w – plane.

A: Given : w=z-11-iz ⇒w1-iz=z-1 ⇒w-iwz=z-1 ⇒z+iwz= w+1 ⇒z1+iw=w+1 ⇒z=w+11+iw

Q: P(Z) (2) Let P(Z) = a + bz + cz² and f dz = = $c P(Z) Z² dz = f P(Z) dz = 2πi Z3 where C is the…

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Q: M2. Let C be the positively oriented circle |z1|-2 in the complex plane. Which of the following is…

A: Given C is the positively oriented circle  in the complex plane. We need to find the value of line…

Q: 2 Green's theorem, evaluate ((+) dx + 3xy dy where C is the circle * +y = 4.

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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: Prove that the equation of any tangent to the circle x\power{2}+y\power{2}-2x+4y-4=0 is of the from…

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Q: 2e² Let f(z) Let c be the (z-7)(z- 9) circle |z| = 11 in the counter-clockwise direction. Find…

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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: Using Euler's equation, show that-: zSinø z{(KØ)} = z2 – 2zCosØ +1

A: The solution is given below

Q: 3. Use Green's Theorem to show that to where C is the unit circle x² + y² = 1 in the…

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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…

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Q: By using Cauchy's integral formulas evaluate sin Tz2 + cos TZ² dz (z + 1)(z – 2) C and e2z dz (z –…

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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: Q5. Prove that the circle {(x, y), z² + y² = 1} is not homeomorphic to the interval (–1, 1). 1

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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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