Complex Variables : Limits and Differentiability
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3. Give a direct proof that
f ΄(z) = -1 / z2 when f (z) = 1 / z (z ≠ 0).
Use this definition to prove the problem.
dw / dz = lim ∆w / ∆z
∆z→0
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Solution Summary
Limits and Differentiability are investigated.
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We have:
f'(z)= lim (f(z+deltaz)-f(z))/deltaz
deltaz--->0
Now f(z)=1/z, therefore:
f'(z)=lim ...
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