Exponential power of sum

Question

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Hi. I was just wondering if Exponential functions that has a power of sum, can I change it to the a product with both having exponentials in them? This is a little hard for me to explain, so I included a picture together. Is this mathematically accurate ?

Answer 1

And then you can write the right hand part as

$\begin{array}\\ e^{i\pi(0.8525+n)} &=e^{0.8525i\pi}e^{i\pi n}\\ &=(\cos(0.8525\pi)+i\sin(0.8525\pi))(\cos(\pi n)+i\sin(\pi n))\\ &=(-1)^n(\cos(0.8525\pi)+i\sin(0.8525\pi))\\ \end{array} $

Answer 2

Yes, $e^{a+b}=e^ae^b$. That is a property of exponents.