Imaginary power of imaginary

[AntonioLao]

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.

[Profpat]

Well thank God that you and Euler's transendental, irrational, infinite, imaginary brains can understand that.

Personally my brain is lost.

[mkirkpatrick]

You only have to think of the imaginary powers of full consciousness to realize the
infinite potential there.



regards michael.

[AntonioLao]

brain is lost

Cauchy's first integral theorem proved that the sum of all fears is zero. Actually he didn't need the proof, he knew it to be so. See thread on imaginary difference to sum.