Complex analysis conformal mapping

a) Find a bijective conformal mapping that takes a bounded region to an unbounded region b) Prove that a conformal map cannot take a simply connected region onto a region that is not simply connected.

complex analysis

Let f be analytic inside and on the unit circle. Suppose that 0<|f(z)|<1 if |z| = 1. Show that f has exactly one fixed point inside the unit circle. ( note : a fixed point is a point Zo such that f(Zo) = Zo).

Complex number questions

1. Find all the values of z in the form a+bi such that (a),(b),(c) (please see the attachment) 2. Find the real part u(x,y) and determine if it is harmonic. (please see the attachment)

Maximum over the closed unit disc

Find the maximum of e^x^2 over the closed unit disc

Improper Integrals of Certain Functions over (- infinity, infinity)

Improper Integrals of Certain Functions over (- infinity, infinity) Please check attached file. Please provide the detailed explanation.

Improper Integrals of Certain Functions over (- infinity, infinity)

Improper Integrals of Certain Functions over (- infinity, infinity) Please check attached file. Please provide the detailed explanation.

P-value

Do a two-sample test for equality of means assuming equal variances. Calculate the p-value. a. Comparison of GPA for randomly chosen college juniors and seniors: ¯x1 = 3.05, s1 = .20, n1 = 15, ¯x2 = 3.25, s2 = .30, n2 = 15, α = .025, left-tailed test. b. Comparison of average commute miles for randomly chosen student ...continues

Complex Analysis

Please show all logic leading up to answer. (see attachment) Find the image of D = under the map w =

Complex Analysis

Compute all the values of log(1 + i).What is its principal value?

Complex Analysis

Suppose w = f(z) is analytical in C.Show that its real and imaginary parts satisfy the Cachy-Riemann equations. Please show all steps to this proof .