Updates:
Status: Accepted
Comment #1 on issue 1302 by ondrej.certik: Raising complex numbers to
fractional powers
http://code.google.com/p/sympy/issues/detail?id=1302
You can use expand(complex=True):
In [1]: (3+4*I)**(S(3)/2)
Out[1]:
3/2
(3 + 4⋅ⅈ)
In [2]: expand((3+4*I)**(S(3)/2), complex=True)
Out[2]:
⎽⎽⎽ ⎛3⋅atan(4/3)⎞ ⎽⎽⎽ ⎛3⋅atan(4/3)⎞
5⋅╲╱ 5 ⋅cos⎜───────────⎟ + 5⋅ⅈ⋅╲╱ 5 ⋅sin⎜───────────⎟
⎝ 2 ⎠ ⎝ 2 ⎠
But I agree it should be possible to simplify the cos+atan things.
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