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math185-s23:hw6-extra

hw6 #4,#5

4. How many roots does the equation z46z+3=0z^4 - 6z + 3 = 0 have in the disk z<2|z| < 2 ? and in z<1|z|<1?

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

  • f:CCf: \C \to \C, where f(z)=zˉf(z) = \bar z.
  • f:CRf: \C \to \R, where f(z)=z2f(z) = |z|^2 .
  • f:CRf: \C \to \R, where f(z)=Re(z)Im(z)f(z) = Re(z) \cdot Im(z)
  • f:CRf: \C \to \R, f(z)=Re(z3+2z)f(z) = Re(z^3+2z)
math185-s23/hw6-extra.txt · Last modified: 2023/02/23 01:03 by pzhou