Here are the contents of a sage file.
var('z')
C = ComplexField()
i = C(0,1)
X = real(integral(z,z))
print X
X = simplify(X)
print X
Here is the corresponding output
1/2*real_part(z)^2 - 1/2*imag_part(z)^2
1/2*z^2
The first line is already surprising as I expected 1/2 *
real_part(z^2). But it's mathematically correct!
The second line, however, is not correct.
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