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 numbers

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)

Closed unit disc

please see attachment Find the maximum of...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. Let f(z)=P(z)/Q(z) be a rational function where...

Integrals

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. Find the image of D = under the map w =

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

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 .

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 .

Euler's equation

Show that y=(A*e^ix)+(B*e^-ix) can be written as y=C*cosine(x-g) A and B are complex but C and g are real Please show all steps!