Furthermore......what is a complex exponent?...........w/o using trig functions...........but the P theorum.......

Complex Exponentiation

A complex number may be taken to the power of another complex number. In particular, complex exponentiation satisfies

(1)

where  is the complex argument. Written explicitly in terms of real and imaginary parts,

(2)

An explicit example of complex exponentiation is given by

(3)

A complex number taken to a complex number can be real. In fact, the famous example

(4)