Shiva is complete; then why does he get married to Parvati?


This is like asking if God is complete, then why did he create this world. A spider is complete, yet it creates a web by its own saliva, and moves within its own web. Waves rise in the ocean, then where do they go? Are they going somewhere? Why do they rise? Got it? The ocean is complete, yet it comes up with waves.
Shiva and Shakti are the same, that is why the concept of Ardhanareeshwar, who is half Shiva and half Parvati
This is true in all of us. In each one, there is a mother’s DNA and a father’s DNA; a male aspect and a female aspect, and together you become complete. Physically, you may be a woman, but you have your father’s aspect inside of you. Is it that only females are born out of females and males are born out of males? No! Inside each one of you, there is a male aspect and a female aspect. 
Shiva and Shakti are one, yet they are different. Parvati is Shakti (the manifest world, i.e., air, earth, fire, water, air, mind, ego and memory), Shiva is the unmanifest. The form and the formless are married; like your mind is formless, the body is form, and they are married
Yet, it is all just one wave function when you go to Quantum Mechanics; there is no male, no female. However, when you want to have a baby, you cannot say that it is all one Quantum Mechanics, it is different there.
When you want to eat food, Quantum Mechanics does not work there. You should know what to eat and what not to eatn correct? So, the world of differences and the world of unity co-exist, yet they are different. That is why it is said that the unmanifest Shiva Tatva has no parallel, there is no two; it is complete
As Shiva, as a male energy, it is consciousness; then there is female energy, i.e., the manifest universe or the body. When you talk about body and mind, then there are two things, the manifest and the unmanifest. But when you talk about atoms or wave function in Quantum Mechanics, it is all just one vibration. 
When you watch television, you see an episode, but if you see it from another angle, you perceive electronic waves. On the other side, you are seeing an episode, and getting some information; they are not opposite. In fact, they are interwoven in nature. 
This is a little bit scientific; if it does not go in, just relax. At some time, you may get it.
PIf you are a Physics student or interested in Physics, then you will catch it easily.
That is why in ancient India, one had to first understand the five elements. They would say that you do not worry about atman (soul), self or God; save that for a later time. First, learn about the five elements and their special permutations. 
Several years ago, a nuclear scientist had come to the Bangalore ashram. In a satsang, I spoke about the five elements. He said that nobody knew about the fifth element; scientists discovered the fifth element recently. The Greeks knew of only four elements.
I told him that he did not know of the Indian philosophy. Since ancient times, they have spoken of five elements in India. Then I told him about the three types of space; he was startled to know that. I asked him to read Yoga Vasishta; it is published by New York University Press. This knowledge has been there. 
So, first they would say that one should understand the five elements and then go to the next three, i.e., mind, intellect and ego. Then, you will come to the Self, to God; before that, they would say do not even think about it!