Can you be complete when alone...
*My opinion counts too:
My response to this question would have to be "yes" because there are a lot of people in our society who do not want to have a companion because they're interested in living their lives as they choose and having another party in the picture will not work. Many people like to pull up their stakes and go to different areas of the world and experience different lifestyles and scenery. They do not want a mate tagging along because their mate just might not want to do that sort of thing and it could have an adverse affect on any relationship.
There are also people who choose to be alone because they like to study, go to school, belong to the art of acting or they are into musical studies, society functions, etc. and a mate would cramp their lifestyle and their desires to do what they wanted to do with their life. This world is made up of all sorts of personalities, likes and dislikes, and it's everyone's right to live the life they so desire. Some people are in love with work or sports and other functions and having someone to tag along does not attract them at all.
*People need to do what they like:
It's like a writer, they love to sit for hours writing and allowing their imaginations to run wild, many do not care to intermingle with a lot of people because it gets in the way of their writing. Many writers also like to read and they can sit for hours with a good book and never say a word to another person. They kinda forget about the outside world and live in a world to themselves. If they go out to eat, they read or they sit there and write, they could care less about another person being with them because they're never alone.
*Summation:
As to whether a person can be complete when alone, I would say it's up to each individual's liking, and that's okay too, because their likes and talents are what they enjoy in their life and they do not ever feel alone because they are so interested in what has become their companion in life. Many people who are like this type life have been this way since they were very young, and as a child, they had things to entertain them and to make them happy until they never feel like they're alone. They're happy doing what they like to do and they do not need anything to distract them from their likes.