Is it necessary to perform the opening Takbir (Takbirat Al-Ihram) when resuming prayer after having said the Taslim (salutation) mistakenly after two rak'ahs of Dhuhr prayer?

If a worshiper, having made the taslim after two rak'ahs, thinking he had completed the prayer, then remembers, within a short customary period, that he had not completed it, he should return and complete the remaining two rak'ahs, and then perform the prostration of forgetfulness (sujud al-sahw). He is not required to say the takbir to complete the prayer, unless his intention with the taslim was to exit the prayer, believing it to be complete; in which case, he is required to say the takbir. However, if he does not remember until after a long customary period, his prayer is invalidated, and he is obliged to repeat it.