Mobile phone have become a necessity for modern life

不是补语和宾语,是表语.
表语是用来说明主语的身份、性质、品性、特征和状态的,表语常由名词、形容词、副词、介词短语、不定式、动词的-ing、从句来充当,它常位于系动词（be,become,appear,seem,look,sound,feel,get,smell等词）之后.
在这句话里,a necessity for modern life是介词短语用作表语.