Problem 1737 (difficulty: 3/10)

How many zeros do the functions have on the given domain?

(a) \(\displaystyle \sin z=2z^2\),    \(\displaystyle |z|<1\)

(b) \(\displaystyle z^4+z^3-4z+1=0\),    \(\displaystyle 1<|z|<2\)

(c) \(\displaystyle z^6-6z+10\),    \(\displaystyle |z|>1\).

Give me another random problem!