4. How many roots does the equation $z^4 - 6z + 3 = 0$ have in the disk $|z| < 2 $? and in $|z|<1$?

5. Recall that the definition of a general open map $f: X \to Y$ is that for any open set $U \subset X$, $f(U)$ is open in $Y$. Are the following maps open? You may sketch your reason.

• $f: \C \to \C$, where $f(z) = \bar z$.
• $f: \C \to \R$, where $f(z) = |z|^2 $.
• $f: \C \to \R$, where $f(z) = Re(z) \cdot Im(z)$
• $f: \C \to \R$, $f(z) = Re(z^3+2z)$