Exponential Form; Identity Transformation

Using the exponential form {see attachment} of z, how that the transformation {see attachment} which is the sum of the identity transformation and the transformation discussed in the attachment, map circles ... See attachment for complete question.

Linear Fractional Transformation

Find the linear fractional transformation that maps the points ... {see attachment}

Linear Fractional Transformation and Transformation of Imaginary Axis into Curve

Find the linear fractional transformation that maps the points {see attachment}. Into what curve is the imaginary axis x = 0 transformed?

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 ad-bc≠0, be any linear fractional transformation other than T(z) = z. Show that T^-1 = T 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.

Cauchy's Formula

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.

Analyticity : Cauchy-Riemann Equation and Antiderivatives

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 three questions.

Analytic Functions

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

Conformal Mapping

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.