1. Show that w = 2 + the w-plane. NI maps the half circle | 2...

Question

Question

1. Show that w = 2 + the w-plane. NI maps the half circle | 2 = 1,0 <<n in the z-plane to the line segment -2<u<2 in

Answer 1

Answer #1

half circle: /Z1 =1. solution: W= Z1 / 2 > z=eie OLOST Waeieteit Coso tisino tloso - isino = 2.03 e oLock. under the Hence im

Answer 2

Similar Homework Help Questions

(c) please Tz that 1. Find the most general linear fractional transformation w = maps the...

(c) please Tz that 1. Find the most general linear fractional transformation w = maps the region A into B : (a) A = {l-1 <1}, B = {Im w >0} (6) A = {lz| <1}, B= {Rew >0} (c) A = {]z – al < R}, B = {Rew 5-3}
5. The problem may be a challenging problem. We define and our goal is to show...

5. The problem may be a challenging problem. We define and our goal is to show that f maps the upper half-plane {z : Im(z) >0) to the unit ball (i) Show that if ż-x + iy, then f(x + yi)-u(z, y) + iv(z, y) where ii) Show that the function maps the real axis y -0 to the unit circle. (Hint: Compute (u(x, 0))2 + (v(,0)2) (Bonus Extra 1 point for the homework grade) (iii) Show that f maps...
Consider the Laplace equation on a circle of radius a around the origin of the xy-plane:...

Consider the Laplace equation on a circle of radius a around the origin of the xy-plane: p?u=0, Osr<a, -Isosa. The boundary condition is u(a,0)= p cos?o, with p a positive constant. Find the solution u(r,o) by separation of variables. Require that the solution is finite at r = 0, and that the solution is continuous with a continuous derivative at 0 = Ín. To check your solution, set r = a and 0 = 0. You should get u(a,0) =...

Plane Curves Find T, N, and K for the plane curves in Exercises 1-4 1,/r(t) ti...

Plane Curves Find T, N, and K for the plane curves in Exercises 1-4 1,/r(t) ti (In cos j, /2 <t< T/2
1. For pdf f (r, y) = 1.22, 0 < x < 1,0 < y <...

1. For pdf f (r, y) = 1.22, 0 < x < 1,0 < y < 2, z +y > 1, calculate: EY) and () E (X2)
Problem,4 Verify that w = f(z) = (z? 1)1/2 maps the upper half-plane Inn(z) > 0 onto the upper ha...

Problem,4 Verify that w = f(z) = (z? 1)1/2 maps the upper half-plane Inn(z) > 0 onto the upper half-plane Im(w) > 0 slit along the segment from 0 to i, a nonpolygonal region. (Use the principal square root throughout.) Hint: The desired non-polygonal region can be obtained as a "limit" of a sequence of polygonal regions.) Problem,4 Verify that w = f(z) = (z? 1)1/2 maps the upper half-plane Inn(z) > 0 onto the upper half-plane Im(w) > 0...

Let X be a random variable with a density function given by 2 NI W x...

Let X be a random variable with a density function given by 2 NI W x – 1 < x < 1 f(x) = 6e elsewhere a) Find the density function of Y = 3 – X. b) Find the density function of Y = X2.
Please show step by step how they got (1-4+(9/2))k^2 = 1 on the last line. Find...

Please show step by step how they got (1-4+(9/2))k^2 = 1 on the last line. Find the points on the hyperboloid x2 - y2 + 2z2 = 1 where the normal line is parallel to the line that joins the points (3,-1,0) and (5,3,6). Then f(x,y,z)= x2 - y² + 2z? fe(x,y,z) = 2x 1,(x,y,z) =-2y f:(x, y, z) = 42 Comment Step 3 of 5 A Then yf(x, y, z)=< 2x - 2y, 4z > Let (xo, Yo, 2.)...
Let S = {a, b}. Show that the language L = {w EX : na(w)<n(w) }...

Let S = {a, b}. Show that the language L = {w EX : na(w)<n(w) } is not regular.

6. Let α be such that Icel < 1 . Let φ,(z) = ,,. Show that...

6. Let α be such that Icel < 1 . Let φ,(z) = ,,. Show that φα(z) maps B(0, 1) zEC: lzl 1) one-to-one onto B(0, 1) and that the inverse map φα(z)-1 is φ,(z). 2