4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute : cos 3z dz (z-1)? (z-3)

Q: 3Q: If z₁ = 1.5 cisand z₂ = 4 cis(-7) find and express it in the rectangular form.

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Q: Explain how you can find the coordiantes of a point 1/8 of the way from point A to point B.

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Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: Let C be the circle given by x² + y² = 1. Evaluate √(-2x²y + cos x)dx + (2 xy² + y²e³)dy going in…

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Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

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Q: 5. Is the point (2, 7) on the circle defined by (x – 2) + (y – 7)2 = 4?

A: Given equation of the circle is: (x-2)2+(y-7)2=4 Given point is: (2,7) Substituting,x=2,y=7 in given…

Q: Evaluate 12x-7 dz where (2213) (2-1)² Cis the circle Z = 2

A: Approach to solving the question:  Detailed explanation:

Q: (b) Evaluate 2 + 5z zdz, 22 — 2х — 3 - where C' is a circle |z + 2| = 2.

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Q: #3. Find 2²43 (2²4)(2+i) & с circle 121=3 dz, where C is the

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Q: Find the image of (4,-1) obtained by translating 4 units up, followed by a reflection over the…

A: We have to find the image of (4,-1) obtained by translating 4 unit up and then reflection over y…

Q: Find z,(-1,2) if z=In(5x°y²+2y*). Answer:

A: We can find the answer as below.

Q: c. Evaluate f 3x ds, where C consists of arc C₁ of parabola y = x² from (0,0) to (2,4), followed by…

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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: + 4z 53. Use (7.8) to evaluate dz around the circle |z – 2i| = 2. - z4 + 8z2 + 16

A: Given,  ∮z3+4zz4+8z2+16 dz  around the circle z-2i=2

Q: 3. Use the Secant method on the circle function (x + 1)²+(y – 2)²= 16 to %3D find the intersection…

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Q: Q6. Evaluate (2yx² - 4x)ds, where C is the lower half of the circle centered at the origin of radius…

A: check belowExplanation:Step 1:Step 2:Step 3: Step 4:

Q: JA- IF f(x) = |Vx- 4, g) x, Find fog(x) Then graph it & determine (domain ,rang Vi- 2cotx B- Granh…

A: Find your answer below

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: Let f(-) = let 1 „Let C be the circle 2 = 9n the counter-clockwise direction. What is 2ni |f(2) de

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