After replace %i to polarform(%i) or domain:complex; we get correct result:

(%i1) polarform(%i)^(4/3);

(%o1) (sqrt(3)*%i)/2-1/2

(%i2) rectform(%);

(%o2) (sqrt(3)*%i)/2-1/2

or

(%i3) domain:complex;

(%o3) complex

(%i4) (%i)^(4/3);

(%o4) (-1)^(2/3)

(%i5) rectform(%);

(%o5) (sqrt(3)*%i)/2-1/2

Other example: integrate(exp(x^5),x,0,1)

Wrong:

(%i6) domain:complex;

(%o6) complex

(%i7) integrate(exp(x^5),x,0,1);

(%o7) (%e^((2*%i*%pi)/5)*(gamma_incomplete(1/5,-1)-gamma(1/5)))/5

(%i8) float(rectform(%)),expand;

(%o8) 0.37851290892278-1.164942948399964*%i

Correct:

(%i9) assume(k>1)$ declare(k,odd)$

(%i11) sol:integrate(exp(x^k),x,0,1);

"Is "(k-1)/k" an "integer"?"n;

(%o11) (gamma(1/k)/(-1)^(1/k)-gamma_incomplete(1/k,-1)/(-1)^(1/k))/k

(%i12) subst(k=5,sol);

(%o12) (gamma(1/5)/(-1)^(1/5)-gamma_incomplete(1/5,-1)/(-1)^(1/5))/5

(%i13) float(rectform(%)),expand;

(%o13) 1.1102230246251565*10^-16*%i+1.224893503635311

(%i14) realpart(%);

(%o14) 1.224893503635311

(%i15) quad_qags(exp(x^5), x, 0, 1);

(%o15) [1.224893503635311,5.5812865751276883*10^-11,21,0]

Aleksas D