imaginary i = 0+1i

exp(I)         =0.54+0.841i
cos(1)+i sin(1)=0.54+0.841i

ln(exp(I))=0+1i

exp(I*PI)=-1+1.22e-16i

log(I)=0+1.57i
I*PI/2=0+1.57i

I^I          =0.208+0i
exp(I*log(I))=0.208+0i