1. Let z and z' be points in C with corresponding points on the unit sphere Z and Z' by stereographic projection. Let N be the north pole N(0,0,1). a) Show that z and z' are diametrically opposite on the unit sphere iff z(z bar)'=-1 ps. here z bar means conjugate of z b) Show that the triangles Nz'z and NZZ' are similar. The
Projective Geometry Problem 4 Let C be the curve in a complex affine plane E. Find the infinite points of C, i.e. the points of the projective closure of that lie on the hyperplane at infinity. See attached file for full problem description.
A) Prove that sum(z^n/n) converges at every point of the unit circle except z=1 although this power series has R=1. b) Use partial fractions to determine the following closed expression for c_n c_n=((1+sqrt5/2)^n+1 - (1-sqrt5/2)^n+1)/sqrt5 Ps. Here c_n are Fibonacci numbers defined by c_0=1, c_1=1,.... c_n=c_n-1 + c_
A) Graph the model b) Find the heights of the cable at the towers and at the midpoint between the towers, and c) Find the slope of the model at the point where the cable meets the right-hand tower y = 18 + 25cosh x/25, -25 ≤ x ≤ 25
Perform the following complex number multiplication and write the answer in standard form: (-3+3i)(2-i)
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1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56. 2. Solve log(2x + 3) = log(4x) + 2, for x giving the answer correct to 3 significant figures. 3. For a thermodynamic process involving a perfect gas, the initial and final temperatures are related by: T1 exp(^s/Cp) =
Please give details of soln |z-i| + |z| = 9
|z|= |z-i| z = x + yi
Sqrt 7x + 29 = x + 3 keywords: complex
Simplify the complex number i^59 as much as possible
(-6 -4i)(1 - 5i)
1.Find the vertex form of the quadratic function g(T)=2T^2-4T+5 and determine the coordinates of this functions vertex vertex form_______________ the vertex______________ 2. solve problem following equations algebraically showing all work and steps and solutions -2X^4+6X^2-4=0 X=__________________ 3.showing all
(3- 2 principle square root 7) (3+2 principle square root 7)
Please see the attached file for full problem description. Show the following complex numbers on an Argand diagram: Given that the equivalent impedance of parallel complex impedances in an electric circuit is given by: calculate the equivalent impedance br the following circuit.
(See attached file for full problem description) 1. simplify each of the following: giving your answer as a complex number in polar form: 2. Convert the following complex numbers in polar form to rectangular (a+jb) from:
1 Find the real and complex solutions of these cubic equations. a) (z-3)(z2-5z+8)=0 b) z3 - 10z2- 34z- 40 = 0, given that 3-i is a root (solution). 2 Solve the equation z3 = 125 cis 45 3 Consider the complex number: z = = cos + z sin a) Use De Moivre's theorem to find z2, z4 and z6. Leave your answers in polar form. b) Pl
Given this expression: (6 - 3i) - (-2 + 7i) How can you perform these operations and then use standard form to write the result.
Singularites (See attached file for full problem description)
Indicate which answer is a simplification. (See attached file for full problem description)
Question 1 Multiple Choice The two sides of a right triangle have lengths 2.92 and 3.98. Find the hypotenuse. □ 6.90 □ 3.34 □ 4.94 □ 3.20 Question 2 Multiple Choice An equation used in the study of protein molecule is In A+ In h - In(1 - h) Solve for
Let be curves in an n open set U. suppose is homotopic to and is homotopic to. Show that is homotopic to . Let where h(z) is holomorphic on an open set U, and h(z) for . Let C be a closed curve homologous to 0 in U such that . Show that Please see the attached file for the fully formatted problems.
Apply DeMoivre's Theorem to solve the following: *any angles that are multiples of pi/6, pi/4, pi/3, pi/2 or pi must be converted back into regular complex form! 6. (-1-i)^4 7. (-4sqrt3 + 4i)^1/3 8. (2(cos pie/3 + i sine pie/3))^5 9. z^4 +8sqrt3-8i=0; solve for z
All decimal answers need 4 place values beyond the decimal. 2. (-3 + 2i)² 3. 2i * 3 convert the following to polar form: *radian mode 4. -12 5. 6-3i
6. Please explain step by step Apply DeMoivre's Theorem to find (-1+i)^6 * change to polar form first You will recognize the angle, so put in the correct value of sine and cosine to reduce back to simple complex form 7. Find the fourth roots of 16(cos pi/4 + i sine pi/4) ; n=4 Please explain in detail 9 solve for
If f is entire and if, for some integer there exists positive constants A and B such that for all z, then f is a polynomial of degree at most k. (Hint, use the function Prove that and use induction on k.)
Suppose ... has radius of convergence R. Find the radius of convergence of: ? ? Please see the attached file for the fully formatted problems.
Complex Analysis : Integration, Primitive and Fundamental Theorem of Calculus and Cauchy's Closed Curve Theorem
Compute the integral in each of the following three ways: ? Directly, by integrating the function along C. ? By finding a primitive and using fundamental theorem of calculus ? By integrating the same function along the straight line from -1-i to 1+I and using Cauchy's closed curve theorem. Please see the attached file
(See attached file for full problem description with symbols and equations) --- Let for . Prove in the following two ways that f has no primitive: a) Assume that f has a primitive F (i.e. these is an entire function F with F'(z)=f(z) for all z). Show that f then would have to satisfy the Cauchy-Riemann equations. Check t
Use definition of limit to prove .... Please see the attached file for the fully formatted problems.