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Hi

var('a,b,z')
assume(z,'complex')
assume(a,'real') ;assume(b,'real')
f(a,b,r)=(a^2 + b^2 - sqrt(a^2 + b^2 - r^2) * sqrt(a^2 + b^2) * sqrt((a^2 + b^2 - r^2) / (a^2 + b^2))) / (a - I*b)
show(f)
show(f.simplify_full())

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