Linear Fractional Transformations and Implicit Form

Find the bilinear transformation that maps the distinct points {see attachment}

Linear Fractional Transformations and Implicit Form

Let T(z) = (az+b)/(cz+d), where {see attachment}, be any linear fractional transformation other than T(z) = z. Show that {see attachment} only if d = -a.

Complex Variable Class - Undergraduate 500 Level

Compute c∫ (e^cosz)(logz)dz where c is the positive oriented circle with center z0=1 and radius 1/2. Please see attached.

Complex Variable Class - Undergraduate 500 Level

Use Cauchy's formula for the derivative to prove that if f is entire and |f(z)|≤ A|z|² + B|z| + C for all zεC, then f(z) = az² +bz + c Please see attached for full question.

Complex Variable Class - Undergraduate 500 Level

Let D be a domain in C and assume that f is analytic in D. Decide whether the statements below are true or false and give a short reason for your answer. a) If there exists an open subset U of D such that Im f≡0 in U, then f is constant in D. Please see attached for all questions.

Complex Variable Class - Undergraduate 500 Level

Show that if f in analytic in {z: |z| < 1} and if Im f(1/k)=0 for all k=2,3... then Imf(x)=0 for -1

Complex Variable Class - Undergraduate 500 Level

Find a conformal mapping from the unit disc Δ(0,1) = {z|z|<1} to D={z:|z|<1}[0,1]. Please see attached for diagram.

Complex Variable Class - Undergraduate 500 Level

Calculate the following integrals: Please see attached for full question.

Complex Variable Class - Undergraduate 500 Level

Calculate the following integrals... Please see attached for full question.

Complex Variable Class - Undergraduate 500 Level

Calculate the following integrals: ∫ from 0 to ∞ x^¼/(x²+9) dx Please see attached for proper format.