2. Find the value of the integral 3z3 + 2 Je (z – 1)(2² + 9)dž, - 1)(2² + 9)' taken counterclockwise around the circle (a) |z – 2| = 2; (b) |z| = 4

Q: Find all harmonic conjugates of u(x, y) = x³ - 3xy² + 2y.

A:

Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: ) Determine the Cartesian Equation perpendicular to the line L1: 4t – 2y = 8, -3t = 6 – 2x with a…

A: Write L1 in Cartesian form. Then find its slope or gradient then use it to find the slope of the…

Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

A:

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: A circle of radius r centered at the point (0,r) in the plane will intersect the y-axis at the…

A: We have to draw the suitable diagram first.

Q: (y + 4)(y² + 8y}Vy² + 8y – 1 dy

A:

Q: x2 + 4y? – xy + 6x – 5y + 1. -

A:

Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

A:

Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

A:

Q: v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located…

A: Let A=(-1,0), B=(2,0), C=(0,2). Now,∫path 1v.dr =∫path 12x2-y2+4dx+5y+3x-6dy…

Q: Let S(x) be a natural cubic spline that passes thorugh the points (-1,1), (0,2), and (1,1). Then,…

A:

Q: The surface 2x2 -2y² – 2z² =1 is identified as

A: The given surface is qudratic surface. Different qudratic surfaces 1)Ellipsoid 2)Hyperboloid in one…

Q: ScF· dĩ, where F(x,y) = (6x - 2y)7+x²7, and C is the line segment Evaluate from (6, -3) to (0, 0).

A: