| Imaginary power of imaginary
Before the discovery of Euler’s identity exp(iq)=cos(q)+isin(q) it is known that the imaginary power of imaginary is real irrational and transcendental. However, since the general form of the identity is exp(±iq)=cos(q)±isin(q) it is also known that imaginary power of imaginary is multi-valued expression, in fact it has infinite values satisfying the given exponential expression.
The infinite real values of imaginary power were first noted by Euler. However, it was also discovered around the same time that the irrational exponent of unity is complex imaginary. Nonetheless, these imaginary values of irrational power of unity are simply theoretical; these quantities cannot be demonstrated or calculated by any actual supercomputers made of a finite amount of material atoms and molecules. This is due to the fact that a physical machine using a finite number of digits to represent numbers can only generate those that are rational and natural.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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Re: Imaginary power of imaginary 
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