a) it is entire in C (complex plane) and has at least two zeros, which are az and a2. b) Evaluate fe f(2)dz along the circle |2| = 2 from (2, 0) to (0, 2) in a counterclockwise direction.

Q: Find and sketch the sets in the complex plane given by (1) z – 3|+|2+ 3=10 IZ (2) |Arg(z)|< t/ 2

A: here we can use directly definition or properties of curve to find that which curve is represented…

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: 18.8. (a). Let y be the contour z = e", - TOST traversed in the %3D positive direction. Show that,…

A: To solve the given question we shall use the following formula: Cauchy integral Formula: Let C be a…

Q: Use the graph to approximate the number of points of intersection of the graphs of y1 and y2.

A: We are asked to find the solution of the graph

Q: 3. Sketch the points determined by the following. (a) Iz+1-i = 2 %3D (b) Im(2z +i) +1=0

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Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: E. Determine the set of points satisfying the condition described by |z – 2i| + |z + 4i| = 10. Then…

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Q: Find parametric equations for the complete parabola x = y2. Answersare not unique.

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Q: Which of the following represents the region of the complex plane defined by |z−2i-3| ≤2? (A)…

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Q: To find the points on the cone z2 = x2 + y² that are closest to the point (5,2,0) , we need to solve…

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Q: Suppose that C = {z:|2| = 1} is the unit circle, followed in the positive (anticlockwise) direction.…

A: Given: C=z:z=1is the unit circle  f(z)=∫cdz4+3z

Q: Describe the following points on the complex plane: (f) i3z = 2-',

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Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

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Q: (b) Show that the equation e- - 2:2 = 1 has exactly two solutions in the disk |2| < 1, and that they…

A: Rouche's theorem: Let f and g be holomorphic function in the region D. Suppose gz&lt;fz on the…

Q: 16)- Consider the quadrature formula 6 | f(x)dx = Af (-6) + Bf(6) -6 If the degree of precession is…

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Q: Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y +…

A: We will use equation of sphere passing through sphere S  and plane P  S+λP =0

Q: The graphs of r +y² + 6x – 24y + 72 = 0 and x² - y' + 6x + 16y - 46 0 intersect at four points.…

A: We have to find distance from given point to intersecting points of given equation. And then add all…

Q: ») Shade the region in the complex plane defined by {rec: s |z+ 2+ 2i <1 4i E C

A: Complex plane

Q: Among all the points on the graph of z = 10 − x2 − y2 that lie above the plane x+ 2y + 3z= 0, find…

A: We have, z = 10 - x2 - y2 and equation of plane is , x + 2y + 3z = 0 The required point on z = 10 -…

Q: Let S be the quadric with equation 36x² – 4y? – 9z2 – 36x = 0 - - (a) Classify the graph of S. (b)…

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Q: z= 2e'+i

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Q: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: Sketch the solid described by the given inequalities. 3sps 4, os ps a/3, 0S0SR 1.5 21.0 0.5 00…

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Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of…

A: Given in a circle of radius r, there are two chords AB and AC such that AB=2AC. Also, the distance…

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: 1. Find an equation for the plane through Po (0,2,-1) perpendicular to n = 3i - 2 j- k ?

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

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: Describe the set S of all points in complex plane satisfying Re (2+ i)z +1) > 0

A: Given  inequation is                                                Re(2+i)z+1&gt;0 let…

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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Q: Show that for every real number k the plane x - 2y + z + 3 + k(2x - y - z + 1) = 0 contains the line…

A: Show that for every real number k the plane x - 2y + z + 3 + k (2x - y - z + 1) = 0 contains the…

Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: a) Find the equation of the plane th

A: The question is taken from the plane in which we have to find the equation of the plane and integral…

Q: Describe the following points on the complex plane: (9) i3Im( (1+i)z ) = 2Re(iz +2).

A: Solution:

Q: Part (a) Evaluate 100e dz, where C is the polygonal path consisting of the line segments from z =…

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Q: Let y = Vxy, y(xo) = yo- %3D %3D Find all points (x0, yo) in the xy-plane where an existence and…

A: Given that  Y'= √xy Y(Xo) =Yo

Q: Prove that using the only the form of the given equation (no graphing) that it is a paraboloid.…

A: We need to prove that the the equation: x2+z2-y4=1 is a paraboloid.

Q: 3 Find the e qu.of Plane that Contains elol; 3) and Parallel to the X-2 Plane and PerPendicular to…

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Q: By means of Lagrange's formula, prove that 1 Yo = - 1 - [2 (y₁+y_₁). (Y3 - y₁) 2 -Y₁) - 2 (Y-₁-y-3)…

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Q: (i) Sael-²dz, where C is the anticlockwise unit circle |2| = 2. (ii) ſadz, , where C is the…

A: As per our guidelines we supposed to answer only three subpart in case of a multi part question.

Q: What are the perpendicular generators on (D) 등 =D3 %3D (P) -= of the surface

A: Given equations are  x216-y24=z ......(1)x3=y2=z-4  ......(2) Equation of generators of the…

Q: Prove that three points (x1, yl), (x2, y2) and (x3, y3) are collinear ( on the same straight line)…

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Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

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Q: Among all the points on the graph of z = 10 - x2 - y2 that lie above the plane x + 2y + 3z = 0, find…

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Q: ind the equation of the parabora y= ax^2 +bx +c that passes through points (0,3) (1,-4) (-1,4)

A: Consider the equation of parabola is given as in the question and passing through the points (0, 3)…

Q: Find the set of points that is satisfied the condition described by |z – 2i|+ |z + 4i| = 10

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Q: Find a parametric representation of the solution set: x1 – 2x2 – 8x3 = 0 3x1+ 2x2 = 0

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