- #1
SNOOTCHIEBOOCHEE
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Homework Statement
If f1 and f2 have residues r1 and r2 at z0. show that the residue of f1+ f2 is r1 + r2
The Attempt at a Solution
Res(f1, z0) = limz-->z0 (z-z0)f1(z) = r1
Res(f2, z0) = limz-->z0 (z-z0)f2(z) = r2
now calculate Res(f1+f2, z0)
=
limz-->z0 (z-z0)(f1(z)+ f2(z))
= limz-->z0 (z-z0)(f1(z))+(z-z0)(f2(z) = r1+ r2
Is it really this easy? i must be doing something wrong