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**1. The problem statement, all variables and given/known data**

If f

_{1}and f

_{2}have residues r

_{1}and r

_{2}at z

_{0}. show that the residue of f

_{1}+ f

_{2}is r

_{1}+ r

_{2}

**3. The attempt at a solution**

Res(f

_{1}, z

_{0}) = lim

_{z-->z0}(z-z

_{0})f

_{1}(z) = r

_{1}

Res(f

_{2}, z

_{0}) = lim

_{z-->z0}(z-z

_{0})f

_{2}(z) = r

_{2}

now calculate Res(f

_{1}+f

_{2}, z

_{0})

=

lim

_{z-->z0}(z-z

_{0})(f

_{1}(z)+ f

_{2}(z))

= lim

_{z-->z0}(z-z

_{0})(f

_{1}(z))+(z-z

_{0})(f

_{2}(z) = r

_{1}+ r

_{2}

Is it really this easy? i must be doing something wrong

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**