Where is f(z) = 1/(z³+1) analytic and what is its derivative?

[MEM33]

Homework Statement

Determine the set on which f(z) = 1/(z^3 +1) is analytic and compute its derivative.

Homework Equations

Hint: you do not need to appeal to the Cauchy-Riemann equations

The Attempt at a Solution

Total stuck with this one. everything we have done this far has been using the c-r equations.

Thanks for any input.

 

[Mute]

Ask yourself:

1) Are there any values of z for which f(z) is not defined? If so, what are they, and what does it tell you about the analyticity of the function?

2) When can you treat taking a derivative of a complex function $\frac{df(z)}{dz}$ just like taking a derivative of a real function?

 

[voko]

Are the function and derivatives defined everywhere?