fiora
Aug 12, 2016

#2**+2 **

fiora
Nov 15, 2018

#5**+1 **

Thanks guest fort spoting my mistake. I am sorry, I was doing another homework and didn't double check my typing.Yeah , you are right，the correct formula for sin(z) is sin(z)=sin(x+iy)= sin(x)*cosh(y)+i*cos(x)sinh(y). The image of strip R under mapping f(z)=sin(z) is quadrant+the fourth quadrant+**the positive real axis of complex plane.** Let w=f(z),then Re(w) is the set positive number and Im(w) is real number.Then the image is an open set,isn't it? Where the definition of open set is **A set is open if all its points are interior points,**and the definition of interior point is **A point a ∈ G is an interior point of G if some open disk with center a is a subset of G.** And **open disk is the inside of this circle with center a and radius r; we use the notation D[a,r] := {z ∈ C : |z − a| < r} .**

See a similar problem posted on stack exchange

https://math.stackexchange.com/questions/1082250/determine-the-image-of-the-strip-s-consisting-of-all-points-z-with-frac

I consider the last answer as correct answer in the preceeding link.

See my instuctor's answer to his sample test problem

follow the link, see problem 5

fiora
Oct 26, 2018