Rouché's theorem - Wikipedia, the free encyclopedia
First by the fundemental theorem of Algebra f has 5 zero's including multiplicity and Consider the Unit Disk.
Define and note that g(z) has 5 zero's in the unit disk (i.e 0 is a root of multiplicity 5)
Now lets check Rouche's theorem
on the boundry of the unit disk
on the boundry so they gave the same number of zero's on the unit disk.
So f has 5 zero's inside the unit disk. Yay