
theorem Th16:
for x be Complex, r be natural Number st x <> 0 holds (x|^r)" = x"|^r
proof
    let x be Complex, r be natural Number;
    assume A1: x <> 0;
    reconsider y = x* x" as Complex;
A2: y = x / x by XCMPLX_0:def 9 .= 1 by A1,XCMPLX_1:60;
    x|^r * (x")|^r = y |^r  by NEWTON:7
     .= 1 by A2,NEWTON:10;
    hence thesis by XCMPLX_1:210;
end;
