9. Let f(z) z4 +6z2 13. Find the residue of z2/f(z) at the zeros f(2)=0 which...
Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular form. 2. Calculate Z1 - Z2 in rectangular form. 3. Calculate Z3 + Z4 in polar form. 4. Calculate Za - Z5 in polar form. 5. Calculate Z1Z2-Z3 in rectangular form. 6. Find ZsZ7 in polar form. 7. Find Z7Zs in rectangular form. 8. Find ZsZs+Z7 in rectangular form Reduce the following to rectangular form. 10. Z1/Z2
Problem 8 (15). Let f(2) 2+1)(22 + 2) (a) Find the residue of f(z) at the point 2 = 1. (b) Find the residue of f(z) at the point (c) Evaluate the integral P.V (r21)(r22) Problem 8 (15). Let f(2) 2+1)(22 + 2) (a) Find the residue of f(z) at the point 2 = 1. (b) Find the residue of f(z) at the point (c) Evaluate the integral P.V (r21)(r22)
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes' Theorem. , where S is the up 10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y...
Question 5. Let f(2) = for z e H4 = {z : Im z > 0}, the open upper half-plane of C. 2+i [2]a) Show that f maps H4 into the open unit disc |2| < 1. Hint: compute |f(2)|² for z e H4. [3]b) Show that ƒ maps the boundary of H onto the boundary of the disc |2| <1 minus one point. What point is missed?
3. Find the residue at 2-0 of the function f(z) 2142
9. (a) Let P1(21, 91, zı), P2 (22, 42, z2),P3 (13, 93, 23) be three non-collinear points in R, that is, three points which do not all lie on a straight line. Then the equations of the plane through these three points is: 2 y 21 1 = 0 22 Y2 22 1 2 1 2141 I3 Y3 23 1 Page 1 (b) Find the equation of the plane through P1(1,2,2), P2(1, 2, -1), P3(0,1,2)
Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x> 0, y> 0 and z> 0 )j+ (3z + 7)k be the velocity field of a fluid. Let B be the Determine the flux of F through B in the direction of the outward unit normal Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x>...
5. Prove that f(z) = (2+1/2) is a conformal map from the half-disc {z = x +iy : 2< 1, y >0} to the upper half-plane. (Hint: The equation f(z) = w reduces to the quadratic equation z2 + 2wz +1 = 0, which has two distinct roots in C whenever w # £1. This is certainly the case if WE H.
Let f(z) z2 and g(z)-z-2, find: a. (fo g)(z) = [ Preview b, (go f)(x) c. (fo g)(-)-1 d' (g of)(-1) = Get Help: Preview Video eBook Points possible: 1 This is attempt 1 of 1. 閂亩□
7. Let S be surface, oriented upward, given by the graph of f(x, y) 2 - z2 -y2 which lies over the unit disk in the ry-plane. If F(, y,z (-4x+ 1 + 3y2 1 +3y2 7. Let S be surface, oriented upward, given by the graph of f(x, y) 2 - z2 -y2 which lies over the unit disk in the ry-plane. If F(, y,z (-4x+ 1 + 3y2 1 +3y2