Singularities of a Complex Function

[ThLiOp]

Homework Statement

What are the region of validity of the following?

1/[z²(z³+2)] = 1/z³ - 1/(6z) +4/z¹⁰

Homework Equations

The Attempt at a Solution

Knowing that this is the expansion around z=0, I am trying to find the singularities of the complex function.

Which is when z²(z³+2) = 0

I have z = 0, then (z³+2) = 0

(z³+2) = 0

z³ = -2 = r³e^i3θ

In order to find r, would I take the absolute value of z³?

r = |z³| = |-2| = sqrt[(-2)²] = 2?

 

[SteamKing]

You should review the algebra of the roots and powers of a complex number:

http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Roots.aspx

 

[haruspex]

r = |z³|

I don't think that's what you meant. Try again.