Question about the argument in a Complex Exponential

[Haku]

Homework Statement

e^-iwt = ?

Relevant Equations

Eulers formula

I know that e^-ix = cos(-x)-isin(x), but if we have e^-iwx does that equal cos(-wx) - isin(wx)?
Thanks

 

[romsofia]

Sure, why not? Just do a u-sub. Let $u = wx$ then you have $e^{-iu} = \cos u - i\sin(u)$. Also, remember that cos is an even function, so you can drop the negative inside your argument!

 

[Office_Shredder]

If w is supposed to be a fixed complex number, you might prefer to rewrite the expression a bit before applying Euler's formula to it. But the statement is certainly true, nothing about Euler's formula requires x to be a real number to begin with.