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"Imaginary power" is similar to "imagination power" in that they both have a form of imagine in them and they both have the word power and in that they mean the same thing.
Imaginary power occurs when the imaginary atoms in your brain- "fakeons" gather up to a density 1 gazillion fakeons per facial square inch. Some theorists theorize they come from Alternate Universes I Seriously Hope Do Not Actually Exist. They then achieve phony escape velocity, and can be falsely directed in whatever direction you put your mind to. (If you watch TV, your imagination will be impaired beyond logic, so you can't do this.)
When somebody with fakeons at phony excape velocity tells them to imaginarily do something, they go right to the task and imaginarily do whatever the person wants. Some people can make cakes, others can make historical figures! Just yesterday Mark Twain used his fakeons to make Oscar Wilde.
Imaginary power is more efficient than nuclear fusion, but less efficient than nyucyular fission
edit Proof of the Existance of Imaginary Power
The power dissipated when a current I is passed through a resistance R is given by
Note that since the power is leaving the resistor, P is negative. As R is pure real (we are considering a system without capacitance or inductance), I must therefore be pure imaginary. For example, if P=-16 W and R=4 Ω, then I=2i A.
If we supply an additional real current, then I has a non-zero real part (We could supply an additional 1A to the example above so that I=2+2i A). This means that P could be complex, or even pure imaginary. (In the example we have been using it comes out that P=32i W)
This proves the existence of imaginary power.
Imaginary power, first defined by bored academics in at the height of the Great Depression, would seem at first to be merely a scam intended to aid the growing number of unemployed engineering professors chasing the same dwindling pool of imaginary research grants. By delivering the maximum AC current peak at the exact point where the voltage was passing through zero, the illusion of electrical research could be sustained without actually needing enough funding to buy any real, live electricity.
Soon, the potential application of imaginary power beyond the confines of academia and the quest for that "least publishable unit" worth of gibberish, that worth of imaginary "knowledge" for use in self-aggrandizement in the academic press, became apparent.
edit The great depression
During this period the economy as a whole was in Dire Straits, and the people of the Hoovervilles couldn't afford real electricity either. It was decided that the best project to keep them busy was the construction of a series of Hoover Dams on various imaginary streams across the continent, generating imaginary electricity to power the growing collection of imaginary appliances which were all the people could afford. Out of these Hoovervilles came extraordinary imaginary inventions, such as Salt Lake City and inevitably the Mormons, Furbys, and Al Gore.
Imaginary power took Depression-era America by storm, much to the consternation of Edison who resorted to selling direct current as a "No imaginary power here, it's all 100% real energy" marketing tactic.
All of this was to become irrelevant when news of the 1939 onset of World War 2 finally reached the USA at Pearl Harbour in 1942, after three years of vain attempts by Paul Revere to get through on horseback having failed when the horses all drowned.
With all of the nation's imaginary enemies defeated (the US never did consider Europe to be anything more than imaginary at the best of times) the last barrier to world domination was gone.
The technology of imaginary power could now be turned to peaceful purposes.
The most successful of these imaginary-power technological ventures was the creation of virtual memory for computers. A large virtual memory array powered by imaginary power costs virtually nothing to operate, yet serves as a dumping ground for all of the useless information with which computers are bombarded every day.
The one exception: one cannot use the Imaginary-Power PC to do real work - only imaginary tasks. So far, the public has yet to notice the difference.
Imaginary power has solved all of Earth's imaginary problems such as imaginary hunger, imaginary high oil prices, and imaginary reality television, but still hasn't fixed any real problems.
But that doesn't mean scientists aren't still hoping.
edit The dark side...
Some among us use imaginary power for evil instead of good. They are known as Windows users. They have caused imaginary disasters, like the imaginary nuclear explosion that blew up imaginary France in 1110 1011 A.I.C. (After Imaginary Cheese), and the Uncyclopedia!
edit Final thoughts
“Always for good, never for evil”