# Thread: The magnitude of a complex exponential

1. ## The magnitude of a complex exponential

$|e^{iwt}|$ = 1

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

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

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

2. Originally Posted by director
$|e^{iwt}|$ = 1

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

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

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

Have you studied complex numbers? If so, you should know that $|a + ib| = \sqrt{a^2 + b^2}$.

3. mod of a complex number suppose z=x+iy is equal to $\sqrt{x^2+y^2}$

so $|z|=\sqrt{(rcoswt)^2+(rsinwt)^2}$
|z|=r

4. Thank you for the replies.