


2. Shade the region of the complex plane defined by E + 5i : 2 비 42 e c . Jistify your answer.
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?
4. Given: 1 + 2 + vady dx (a) Draw (and shade) the region in the xy-plane that is represented by the integral and the defined region of integration. Do not forget scales and labeling of axes. (b) Write the integral by changing to polar coordinates and evaluate Show we integration step. Exact answer only. Reminder. dA = rdrde 3/5
#1,5,9 and #13,17,21,25 please.
In Exercises 1-12, graph each complex number in the complex plane 3. -2 4i 2 2. 3 5i 7.-3i 8.-5i 6. 7 47 19 7 15 2 11 2 12. 10 10 each complex number in polar form 15. 1 V3i 14. 2 + 2i 16. -3- V3i 3. 1-i 20. -V3+i 18. V5_V5İ 19. V3-3i 17-44i 24. -8-8V3i 22. 2 + Oi 2 23, 2v3-2i 21. 3 +0i V3 1 1 V3 28·16+161 26, 1...
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.
Sketch the region in the xy-plane defined by the inequalities x - 3y2 2 0, 2 x - 5lyl 2 0 and find its area.
Sketch the region in the xy-plane defined by the inequalities x - 3y2 2 0, 2 x - 5lyl 2 0 and find its area.
Sketch the following region in the complex plane: the set of z such that z (32i) 2
The electric field in the region defined by the y-z plane and the negative x axis is given by Ea where a is a constant. (There is no field for positive values of x.) As -x increases in magnitude relative to -0 at the origin, the electric potential in the region defined above is 9) A) a decreasing function proportional to B) a decreasing function proportional to C) constant. D) an increasing function proportional to + E) an increasing function...
(Complex Analysis)
The linear mapping wFUz+p, where α, β e C maps the point ZFI+1 to the point wi-i, and the poin to the point w2-1i a) Determine α and β. b) Find the region in the w-plane corresponding to the upper half-plane Im(z) 20 in 9. the z-plane. Sketch the region in the w-plane. c) Find the region in the w-plane corresponding to the disk Iz 2 in the z-plane d) Find the fixed points of the mapping
The...
“not right but left half plane.” complex analysis
CC be defined by or each real number a, let fo : Prove that if a > 1, then fa has exactly one zero in the right half-plane E C:Ra)o and that this zero is a real number