Analysis of Subsets: Is Re (Real Numbers) Open, Closed, or Neither?

[Fairy111]

Homework Statement

I need to find out whether the subset Re(real no's) of complex no's is open, closed or neither.

Homework Equations

The Attempt at a Solution

Im not really sure how to begin this...any help please?

 

[HallsofIvy]

Homework Statement

I need to find out whether the subset Re(real no's) of complex no's is open, closed or neither.

Homework Equations

The Attempt at a Solution

Im not really sure how to begin this...any help please?

Let x be any real number and consider a neighborhood of it in the complex numbers: \{z | |z- x|< \delta\}. Does that contain any non-real numbers?

 

[Fairy111]

yes i think it does contain non real numbers, so this would imply that it is an open subset?
how would i go about sketching it?