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r := abs(z)^(Re(a)) * exp(-Im(a) * argument(z));
w:= r * abs(z)^(Im(a)*I) * (z/abs(z))^Re(a);

I want to see, that z^a = w.

But simplify(w) gives a wrong result, it differs from w:

tstData:= [z=1+3*I, a=-3+I];
z^a; eval(%, tstData):  evalf(%);
'w'; eval(%, tstData): evalf(%);
'simplify(w)'; eval(%, tstData): evalf(%);

tstData:= [z=-2*I, a=+I];
z^a; eval(%, tstData):  evalf(%);
'w'; eval(%, tstData): evalf(%);
'simplify(w)'; eval(%, tstData): evalf(%);

In the last case simplify(w) results in a purely real value,
while w has a nonvanishing imaginary part.

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