hw6 #4,#5
4. How many roots does the equation z4−6z+3=0 have in the disk ∣z∣<2? and in ∣z∣<1?
5. Recall that the definition of a general open map f:X→Y is that for any open set U⊂X, f(U) is open in Y. Are the following maps open? You may sketch your reason.
f:C→C, where
f(z)=zˉ.
f:C→R, where
f(z)=∣z∣2.
f:C→R, where
f(z)=Re(z)⋅Im(z)
f:C→R,
f(z)=Re(z3+2z)