The magnitude of a complex exponential

May 2010
63
0
\(\displaystyle |e^{iwt}|\) = 1

I've seen this expression a few times but without an explanation. Is the following true:

\(\displaystyle z = re^{iwt} = r(cos(wt) + isin(wt))\)
\(\displaystyle |z| = ( cos(wt)^{2} + sin(wt)^{2} )^{1/2} = (1)^{1/2} = 1\)

I don't have the \(\displaystyle i\) included inside the square root though... Is that by convention? Because we're talking about something that's supposed to have a real value?

Thanks for your help. (Bow)
 

mr fantastic

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\(\displaystyle |e^{iwt}|\) = 1

I've seen this expression a few times but without an explanation. Is the following true:

\(\displaystyle z = re^{iwt} = r(cos(wt) + isin(wt))\)
\(\displaystyle |z| = ( cos(wt)^{2} + sin(wt)^{2} )^{1/2} = (1)^{1/2} = 1\) Mr F says: Yes (overlooking the fact that you have an r that disappears).

I don't have the \(\displaystyle i\) included inside the square root though... Is that by convention? Because we're talking about something that's supposed to have a real value?

Thanks for your help. (Bow)
Have you studied complex numbers? If so, you should know that \(\displaystyle |a + ib| = \sqrt{a^2 + b^2}\).
 
Apr 2010
41
15
India
mod of a complex number suppose z=x+iy is equal to \(\displaystyle \sqrt{x^2+y^2}\)

so \(\displaystyle |z|=\sqrt{(rcoswt)^2+(rsinwt)^2}\)
|z|=r
 
May 2010
63
0
Thank you for the replies.
My question about the imaginary unit was silly so please disregard.

I figured out what I wanted.

PS. Slovakiamaths, sorry but I don't have enough posts to reply to your PM. I'm not studying in Poland though.
 
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