(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working. (7) Let 0くa 〈 b 〈 c 〈...
Help with detail answer. Consider the following: w g(z)where w is the fractional linear (Mobius) transformation Describe and sketch the image set of g(B) if B is the annulus { z ε ¢ : 1 < Izi < 2} Consider the following: w g(z)where w is the fractional linear (Mobius) transformation Describe and sketch the image set of g(B) if B is the annulus { z ε ¢ : 1
19. Which of the following statements are always true? (i) Re(2)Im(iz) 0 (ii) Re(iz)Im(z) = 0 (iii) z- Zi Im(z) = 0 (a) (ii) only (b) (i) only (c) (iii) only (d) (i) and (ii) only (e) (ii) and (ii) only
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
Describe in plain english what the following regular expressions match: ab+c [A-Z][0-9]{6} \d+ ([A-Z][a-z]+)+\n([A-Z][a-z]+)+,[A-Z]{2} \d{5}\ Write a finite state machine for each of the previous regexs.
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic definition of derivative operation based on the limiting case as lim Az-0 Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic...
(1) Consider the polynomial map C → C defined by z-Plz) 22 + c, c E C. In class, we proved the following two facts: Suppose lel < 2. If an orbit [z0, 21,22,..} (where zn p"(20)) contains an iterate zn such that 2n2, then the orbit diverges to oo. (Thus if the orbit of zo ever strays outside the disk of radius 2 about the origin, 20 does not belong to the filled Julia set for any p(z) with...
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 following region in the complex plane: the set of z such that z (32i) 2