| eight-fold power symmetry -
02-13-2008, 11:49 AM
Using complex numbers it can be demonstrated that power symmetry exists. A complex numbers z is given by z=a+bi where i is the imaginary unit and a and b are real numbers. Using simple multiplications show that the product of any complex number and its conjugate is always real. However, the power of a complex number can be real, imaginary or complex depending on the degree of its power. And where and when the absolute values of a and b are equal, |a|=|b|, the 4th power is always negative real while the 8th power is always positive real.
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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