Are energy and capital complementary factors of production? Why energy and capital are complementary factors of production?

In the literature of environmental taxation, it's often argued that energy and capital are complementary factors of production. So for instance if price of energy goes up, so will the price of capital. I am struggling to understand the relationship.
You say "energy and capital are complementary factors of production. So for instance if price of energy goes up, so will the price of capital.". I think you might have confused yourself because this kind of positive correlation in prices is not necessarily a property of complements (indeed, often one would expect the reverse to be true).

It is more helpful to think of complementarity as "if the price of energy goes up then the demand for capital will go down" (in much the same way that people will buy less butter if bread becomes more expensive).

The reason for this is not far from that proposed by andersan. Capital is often invested in machines (e.g., computers, robots, trucks, farm equipment) that require energy to operate.

Consider a factory producing cars. It can assemble the car in various ways (a) by having a team of workers (labour) do the work, (b) installing robots on an assembly line, or (c) some combination of the two. If the price of electricity doubles then having a bunch of robots on the factory floor suddenly becomes more expensive because the energy needed to run them became more costly. Thus, the guy who was just indifferent between having a robot and a worker will now strictly prefer to hire a worker and the demand for capital decreases.

Even if you have a business (e.g. long-distance transportation) where you cannot easily substitute capital for labour, there will buy some entrepreneur who is indifferent between buying some capital goods (e.g. planes) to start a business and not. An increase in the cost of energy (e.g. fuel) will reduce the prospective profitability of his firm and thus leave him strictly preferring not to invest.