Phasor help

Thread Starter

testing12

Joined Jan 30, 2011
80


Hello,
I am familiar with Euler identity, however I am not sure how the left side translates into the right side. Could someone please provide some extra detail.
Kinds Regards
 

blah2222

Joined May 3, 2010
582


Hello,
I am familiar with Euler identity, however I am not sure how the left side translates into the right side. Could someone please provide some extra detail.
Kinds Regards
\(cos(w_{0}t) = \frac{1}{2}[e^{jw_{0}t} + e^{-jw_{0}t}]\)

Multiply in using law of exponentials with:

\(e^{j\alpha t}\)
 

WBahn

Joined Mar 31, 2012
29,930
To see where the identity that blah2222 used comes from, consider the following:

\(
e^{j\theta} \,=\, \cos(\theta)\,+\,j\,\sin(\theta)
\;
e^{-j\theta} \,=\, \cos(-\theta)\,+\,j\,\sin(-\theta)
\;
\cos(-x) \,=\, \cos(x)
\sin(-x) \,=\, -sin(x)
\;
e^{-j\theta} \,=\, \cos(\theta)\,-\,j\,\sin(\theta)
\;
e^{j\theta} \,+\, e^{-j\theta} \,=\, 2\cos(\theta)
\;
\cos(\theta) \,=\, \frac{1}{2} \left( e^{j\theta} \,+\,e^{-j\theta} \right)
\)
 

Thread Starter

testing12

Joined Jan 30, 2011
80
I know this is an old post, but i Would like to add to it...
I have a new problem, see below. How is the real part of E1=2 Eo sin (B) z sin (wt) ? in the previous line there was a j in front of all of this, making it all imaginary.
 
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