Farsi is an Indo-European language. Arabic is an Afro-Asiatic language. Farsi is genealogically closer to English than Arabic.
im a fucking idiot.
No, it's a fairly widespread misconception. People also think Turkish is also somehow related to Arabic and/or Farsi whereas Turkish belongs to a yet another language family (Turkic Languages) and is genealogically entirely unrelated.
Farsi has adopted the same alphabet and has some Arabic loan words but it's a very different language. Farsi is an Indo-European language while Arabic is Semitic (Afro-Asiatic).