# How to expand function $\cos(y+i\log{x})$ in powers of $x$?

I have the following, probably very simple question. How can I get $\it{Mathematica}$ to power expand function $\cos(y+i \log(x))$ in powers of $x$? This function obeys a well defined Laurent expansion about $x=0$ and I would like $\it{Mathematica}$ to give $\frac1{x}e^{i y}/2+x e^{-iy}/2$ upon evaluation of

Series[Cos[y + I Log[x]], {x, 0, 1}]


However, the result is

Cos[y + I Log[x]]


i.e. the original expression. I can bet that in some circumstances such expansion worked without any effort from my side.

I wonder what is the right way to obtain the expansion of the function $\cos(y+i \log(x))$ in powers of $x$.

Any help is appreciated.

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One way to get the desired output is to use TrigToExp
TrigToExp[Cos[y + I Log[x]]]