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Hello, @ripple_carry! The easiest way I know of achieving that effect is to explicitly declare the imaginary part of the function to be zero. Just use the imag_part_func argument for function as follows:
var('z')
u = function('u',imag_part_func=0)(z)
v = function('v',imag_part_func=0)(z)
f = u + i * v
show(f.diff(z).conjugate().expand().simplify_full())
This outputs
diff(u(z), z) - I*diff(v(z), z)
Hope this helps!
