Complex Plane

  • #1
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Homework Statement


Screen Shot 2017-08-22 at 7.21.29 PM.png


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!
 

Answers and Replies

  • #2
Ray Vickson
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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##?
 
  • #3
SammyS
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Homework Statement


screen-shot-2017-08-22-at-7-21-29-pm-png.png

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} \ ##.
 

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