Of course science and religion can coexist. But I can't see how science and religion can complement each other. One deals with the natural world and the other deals with a supernatural world or an imaginary world. 

There is the natural or real world (science) and there is the imaginary world (religion). This is like logic and illogic.

Thing is, the imaginary world is entirely man-made and made up. So it has no scientific meaning whatsoever. So it can't complement science because it doesn't have anything scientifically meaningful to say about anything in the natural world.

Even our thoughts are in the natural world. There's nothing supernatural about our thoughts. So even the imagination can be studied scientifically. So what does religion have to say about anything? Nothing, really;

Science doesn't need any help from religion. Religion is afraid of science.