It depends on what you’re talking about, if you mean energy for a system, then yes, this is usually described as energy being imput into the system, where as energy being output by a system is positive.

Not really.
Einstein’s famous equation E=mc^2 showed that matter and energy are related, and one can be converted to the other (assuming suitable circumstances, which are not that easy to obtain). So, if there was negative energy, there should be negative matter, and there is no such thing in our universe.
But wait a minute, you may ask. What about antimatter?
Antimatter is not negative matter, it is matter with reversed charge: the positron for instance is just like an electron but with a positive charge. The positron have positive mass, it is therefore matter.
When a positron meets an electron, they annihilate each other, releasing an energy equivalent to the mass of both the electron and the positron together; so both were still matter.
Cosmological models are talking about dark matter and dark energy, stuff needed to make observations fit with the theories.
One property of dark energy is that it should be a repulsive force. Is a repulsive force a negative energy? If you answer yes, then this may be your negative energy; but then it is more a matter of definition than anything else.
Sorry the answer cannot be more accurate, but it is usually the shortest questions that have the longest and least meaningful answers. And in the case of dark energy, this is a domain where top scientists are still somewhat at a loss.

there are different forms of energy (potential, kinetic, etc.). the energy from one system may counteract or enhance the energy from another system. however, there is no negative energy.

That’s how antimatter was discovered. Read the wiki article about the “Dirac Sea”, and reasoning about negative energy states that led to the hypothesis and discovery of antimatter. Physicists work with the concept of negative energy routinely. Check the next link as an example.
Classically speaking, energy is always positive. Momentum can be negative, but classical newtonian and thermodynamic masses only have positive energy content. It’s like how any real number squared yields only positive reals.

Yes

It is energy to be consumed.

and

Imaginary energy is stored energy ðŸ™‚

It depends on what you’re talking about, if you mean energy for a system, then yes, this is usually described as energy being imput into the system, where as energy being output by a system is positive.

There is positive AND negative energy.

.

Not really.

Einstein’s famous equation E=mc^2 showed that matter and energy are related, and one can be converted to the other (assuming suitable circumstances, which are not that easy to obtain). So, if there was negative energy, there should be negative matter, and there is no such thing in our universe.

But wait a minute, you may ask. What about antimatter?

Antimatter is not negative matter, it is matter with reversed charge: the positron for instance is just like an electron but with a positive charge. The positron have positive mass, it is therefore matter.

When a positron meets an electron, they annihilate each other, releasing an energy equivalent to the mass of both the electron and the positron together; so both were still matter.

Cosmological models are talking about dark matter and dark energy, stuff needed to make observations fit with the theories.

One property of dark energy is that it should be a repulsive force. Is a repulsive force a negative energy? If you answer yes, then this may be your negative energy; but then it is more a matter of definition than anything else.

Sorry the answer cannot be more accurate, but it is usually the shortest questions that have the longest and least meaningful answers. And in the case of dark energy, this is a domain where top scientists are still somewhat at a loss.

there are different forms of energy (potential, kinetic, etc.). the energy from one system may counteract or enhance the energy from another system. however, there is no negative energy.

That’s how antimatter was discovered. Read the wiki article about the “Dirac Sea”, and reasoning about negative energy states that led to the hypothesis and discovery of antimatter. Physicists work with the concept of negative energy routinely. Check the next link as an example.

Classically speaking, energy is always positive. Momentum can be negative, but classical newtonian and thermodynamic masses only have positive energy content. It’s like how any real number squared yields only positive reals.