Incase of customer complaint from one who doesn't want to listen,very tough and arrogant customer,how can you handle such a situation?

i would talk to the customer in a calm way .. ask him to sit down . and tell him if he wants to drink any coffee or lemon juice would be preferable to calm him down .. and listen to his complain and promise to find the best solution and tell him that we as a company wouldn't like to lose such a customer .. 

i might even crack a joke to make his mood swing and get back to get calm 

Remain calm and apologetic look at him/her straight in the eye and try to give a possible solutions to the problem make him feel  that your attention is with him only keep quiet for a moment just listen to him after that again apologized and resolve the problem by also informing him that his complain will be brought up in the management and complement  for his complain this measure the capability of the customer service to know more about the job to avoid such issue.

Offering a glass of water goes a long way. Calm the said customer down. It helps not to contradict his statements rather work around what he's saying. Never antagonize the customer rather feed his ego. And it usually helps if the one answering his queries and complains is someone with an authority so that he would feel very important.