Show that Im(\frac{e^{i \theta}}{1-xe^{i \theta}})=\frac{\sin(\theta)}{x^2-2x \cos(\theta)+1}

zakinutuzi

zakinutuzi

Answered question

2022-01-17

Show that Im(eiθ1xeiθ)=sin(θ)x22xcos(θ)+1

Answer & Explanation

Anzante2m

Anzante2m

Beginner2022-01-18Added 34 answers

Note that
eiθ1xeiθ=cos(θ)+isin(θ)1xcos(θ)ξsin(θ)
=(cos(θ)+isin(θ))(1xcos(θ)+ξsin(θ))(1xcos(θ))2+x2sin2(θ)
=cos(θ)x+isin(θ)x22xcos(θ)+1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?