Complex Plane Fix c in C0 Complex plane without zero Find th

Complex Plane

Fix c in C\\{0} [Complex plane without zero]

Find the derivative of f(z)=z^c

Solution

Solution:let comlex plan c=a+ib

given function f(z)=z^c

we take diffrentiate both side of eq.

   f\'(x)=cz^c-1                              we puting the value of c

f\'(x)=(a+ib)z^a-1+ib