Question

\[\lim_{ z \to -1} z+1\]

Answer 1

so I am struggling with limits in my complex variables course. I don't really understand to show that limits exist...

Answer 2

\[f(z)=u(x,y)+i v(x,y)\]\[u(x,y)=x+1\]\[v(x,y)=y\]\[\lim_{ (x,y) \to (x_0,y_0)}u(x,y)\]

Answer 3

here would I have \(x_0=-1\) and \(y_0=0\) ?

Answer 4

in that case I would have the limit = 0. which then would make the problem I am actually doing)\[\lim_{z\to -1}\frac{iz+3}{z+1}=\infty\]

Answer 5

and finally, \(\infty\) is just a single point right? there is no positive and negative \(\infty\) because when you move to the top of the Riemann sphere, at the very top there is something messed up, not sure if "degeneracy" is the right term, but the point on the sphere no longer corresponds with one point right?