Infinite Strip under Given Transformation ...

Find the image of the infinite strip 0 < y < 1/(2c) under the transformation w = 1/z. Sketch the strip and it's image {see attachment}

Hyperbola; Lemniscate

10. By writing {see attachment}, show that the mapping w = 1/z transforms the hyperbola {see attachment} into the lemniscate {see attachment}

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; Imaginary Axis Transformed

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