def _eval_expand_complex(self, *args):
if isinstance(self.exp, Basic.Integer):
re, im = self.base.as_real_imag()
base = re + S.ImaginaryUnit * im
return (base**self.exp)._eval_expand_basic(*args)
elif isinstance(self.exp, Basic.Rational):
# NOTE: This is not totally correct since for x**(p/q) with
# x being imaginary there are actually q roots, but
# only a single one is returned from here.
re, im = self.base.as_real_imag()
r = Basic.sqrt(re**2 + im**2)
t = Basic.atan(im / re)
if im == 0 and re == -1:
t = S.Pi
rp, tp = r**self.exp, t*self.exp
return rp*Basic.cos(tp) + rp*Basic.sin(tp)*S.ImaginaryUnit
else:
return S.Re(self) + S.ImaginaryUnit*S.Im(self)
