Some people find nasty customers very difficult to deal with. They can be upset for several days after meeting one. If you have this problem, perhaps you could think about it in the following way:
One therapist told about one of her patients, who when she met such a customer thought: YDH, YDH, YDH, which stood for "you damned hag." She never revealed her feelings and smiled as usual but her thought protected her.
There is never any reason to be unpleasant towards others. It is not your fault if somebody is unpleasant towards you. Even if you have done something wrong, the customer should complain in a correct way so that you can rectify the matter, and not treat you badly.
To be horrible towards others is comparable to physical injury and the mental scars may last a lifetime.
But you need not see an angry customer only as something negative. The customer is showing her concern and interest through her anger. It is always good to try to understand why a customer is angry, and consider how you can change your services to avoid similar problems for other customers.
Disgusting behaviour sometimes occurs because a customer doesn't feel well. If this appears to be the case you can comment sympathetically and this may help.
Sometimes, this will not help. Some people are convinced that they are right and that they have a right to be nasty even because of the smallest error, which you may have done. There are even sadistic people, who enjoy tormenting other people. Such people have often themselves been objects of psychological abuse, and now, when they are not victims any more, they enjoy being the tormenter.
Even if the angry customer is obviously not right, you should show that you understand the customer. It is always good to say that you will investigate the problem. Be sensitive, try to understand what the angry customer is trying to say, show compassion. It is often good if you summarize the view of the customer, using the words of the customer, to show that you understand her problem.
It can also be useful to discuss nasty customers with co-workers and friends; their help and support can be valuable.