Sketch the following region in the complex plane: the set of z such that z (32i)...
1. Sketch the region in the complex plane that contains the elements of {Z – 3+i:ze C,1<\2-11 <2} n {z EC: Im(2) >0}. Justify your answer.
In Exercises 1-10 sketch the set in the complex plane described by the inequality inequalities. State whether the set is open, closed, bounded, connected, and/or or a domain. 1. |z-i+34
2. Shade the region of the complex plane defined by <z +4 + 3i : 3 < 3 < 5,2 EC}. Include the appropriate axis labels and any significant points.
Q5. (a) Consider the region in the complex plane defined by: z = x+iy : 1, lul π/3. Draw this region in the z-plane and mark a few points on it of your choice (eg, A, B, C) Now, apply the conformal transformation w-e*. Plot the resulting region and mark the corresponding points (eg., A, B, C.) (b) What is the area (in arbitrary square units) of the figure in the z-plane? What is the area in the w-plane?
Please show work and sketch the bounded region in the xz-plane. Thanks!! Write the set of equations in cartesian form that bound the volume of the solid given below: T/4 (2 sec phi p'sin(o) dp do do Jo Jo Sketch the bounded region in the rz - plane. JO
Sketch the region of the integration, V . Please include the region that is on the z − x plane also. dydzdr = dydzdr dydzdr = dydzdr
1. Sketch the following set of points in the z-y plane: {(x, y) € R2 :(y - x²)(y + |21) >0}
23. Consider the function w(z) = 2-2 (a) Where in the complex z-plane are the poles of w(z)? (b) Determine the first three terms for the Taylor series expansion of w(z) about 0 (c) Identify the region of convergence for the Taylor series of part (b). (d) Determine the general expression for the n'h coefficient of the Taylor series expansion of part (b) 208 INTRODUCTION TO COMPLEX VARIABLES (e) There is a Laurent series expansion for wC) about-= 0 in...
(a) (2 points) In the plane below, sketch the region corresp below, sketch the region corresponding to: {(x, y) - 1<y <2}. Use the convention that, if the boundary of a region is included in the dicated using a solid line. Otherwise, use a dashed/dotted line. Clearly show any 2 and y intercepts on your graph.
7. Find the volume of the region in space, the region beneath z = 4x2 + 9y2 and above the rectangle with vertices (0,0), (3,0), (3,2), (0,2) in the xy-plane. Sketch it 7. Find the volume of the region in space, the region beneath z = 4x2 + 9y2 and above the rectangle with vertices (0,0), (3,0), (3,2), (0,2) in the xy-plane. Sketch it