I think that the Iranians can't be considered to be close to Slavs or any Europeans anymore.
We can't be sure about their physical appearance in the past, but now they do not share much characteristics with the Europeans. The picture provided by Sibiryak shows it all – only few of those girls could pass for European.
They differ to much even linguistically – since they adopted Islam, they adopted thousands of Arabic words and phrases with it.
Their once Indo-European language and culture is now way to overwhelmed with Semitic and other Eastern influences to be considered "brotherly".
Still, their connection to us is, I believe, undisputed.