One roman emperor was particularly bad. he not only had his own mother killed, but castrated then married his favorite slave. to which emperor do we refer?

I believe you are referring to Nero.
He was a Roman emperor known for his cruelty. He disagreed with his mother over something, and then killed her because of that. Sporus is the name of the slave Nero castrated, and then later married, after having killed his own wife.

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