\(\displaystyle{i}{\sin{{\left({x}\right)}}}\) phase shift By Euler's formula, I can

tambustqaze

tambustqaze

Answered question

2022-04-01

isin(x) phase shift
By Euler's formula, I can express i in the following way:
i=cos(π2)+isin(π2)=exp(iπ2)
I wonder if it is legitimate to write
isinx=exp(iπ2)exp(ix)exp(ix)2i
=exp(ix)exp(iπ2)exp(ix)exp(iπ2)2i
=exp(i(x+π2))exp(i(x+π2))2i
=sin(x+π2)
I don't feel like this is right, because it would imply a lot of weird things. So where is my mistake?

Answer & Explanation

mistemePietsffi

mistemePietsffi

Beginner2022-04-02Added 8 answers

In your sleep-deprived delirium, you have said
eixeiπ2=ei(x+π2)
where it is actually
eixeiπ2=ei(xπ2)
It would certainly be strange if isin(x)=sin(x+π2) since one is pure imaginary and the other real for real x.

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?