Complex Plane Homework: Mobius Transformation Advice

[WWCY]

Homework Statement

Homework Equations

The Attempt at a Solution

I'm not sure how to even begin this problem. My notes mentioned something about a Mobius Transformation but that's not something that I've been taught, and certainly not something I'm familiar with.

Any advice would be greatly appreciated!

 

[Ray Vickson]

Homework Statement

View attachment 209496

Homework Equations

The Attempt at a Solution

I'm not sure how to even begin this problem. My notes mentioned something about a Mobius Transformation but that's not something that I've been taught, and certainly not something I'm familiar with.

Any advice would be greatly appreciated!

Start by putting ##\alpha=1, \beta=i## into the expression for ##z(t)##: ##z(t) = 1/(t+i)##. What are the real and imaginary parts of this ##z(t)## for real ##t##?

 

[SammyS]

Homework Statement

Homework Equations

The Attempt at a Solution

I'm not sure how to even begin this problem. My notes mentioned something about a Mobius Transformation but that's not something that I've been taught, and certainly not something I'm familiar with.

Any advice would be greatly appreciated!

or

Rationalize the numerator of ##\displaystyle \ \frac{1+e^{is}}{2i} \ ##, simplify, and compare the result to ##\displaystyle \ \frac 1 {t+i} \ ##.