2. If P (z) is a polynomial and Г is any closed contour, explain why Jr...
Prove that any polynomial p(z) with real coefficients can be decomposed into a product of polynomials of the form az2 + bz + c, where a, b, c ∈ R.
Here you are asked to prove the Fundamental Theorem of Algebra a different way by using Rouché's Theorem. Where n E N, consider the polynomial n-1 Pn (z)z" k-0 Using the circular contour C-[z : zR with R appropriately chosen, (a) prove that pn(2) has (counting multiplicity) precisely n zeros in the open disc D(0, R); (b) also show that Pn(z) has no zeros in C \ D(0, R) Here you are asked to prove the Fundamental Theorem of Algebra...
True or false, if false explain why. In any closed system with P-V work only, G is always minimized at equilibrium.
1. (а) Using an appropriate contour in the upper half plane, find the integral z-1 dz. (z - i)(z+3i)2 If the contour was closed in the lower half plane, explain how your (b) residue calculation would change.
1. (20 points) Let C be any contour from z = -i to z = i, which has positive real part except at its end points. Then, consider the following branch of the power function zi+l; f(3) = 2l+i (1=> 0, < arg z < Now, evaluate the integral Sc f(z)dz as follows: (a) (5 points) First, explain why f(z) does not have an antiderivative on C, but why the integral can still be evaluated. (b) (5 points) Then, find...
Let P(z) be a polynomial of degree n 2 1. Then CA. P(z) is analytic and bounded on C B. P(z) is not analytic but bounded on C C. P(z) is analytic and unbounded on C D. P(2) is bot analytic and unbounded on C
he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1 he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1
Problem (4) Let f(z) denote the function e a f(z) 1 - z Compute f (z) dz where y is any contour that encloses the origin but does not enclose the point z =1 Problem (4) Let f(z) denote the function e a f(z) 1 - z Compute f (z) dz where y is any contour that encloses the origin but does not enclose the point z =1
complex variable question. i need readable handwriting/typing 2. Evaluate the contour integrals, explaining your answers. Give your answers in the form a + bi, where a and b are real. a) R C z 2 dz, where C is any contour which begins at z = 1 and ends at z = 2i b) R C 1 z dz where C is any contour which begins at z = 1 and ends at z = 2i, and does not cross...
Why is this molecule achiral? Please explain with picture, step-by-step instructions. Г / Me