(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that [tex]lim_{z \rightarrow 1+2i} [ix - (x+y)] = -3 + i[/tex].

2. Relevant equations

[tex]lim_{z \rightarrow z_0} f(z) = w_0[/tex] if and only if given [tex]\epsilon > 0[/tex] there exists a [tex]\delta > 0[/tex] such that [tex] 0 < |z-z_0| < \delta \Rightarrow |f(z)-w_0| < \epsilon[/tex]

3. The attempt at a solution

[tex]f(z) = ix-(x+y), w_0 = -3+i, z = x+iy, z_0 = 1+2i[/tex]

I calculated the following:

[tex]|z-z_0| = \sqrt{(x-1)^2+(y-2)^2}[/tex] and

[tex]|f(z)-w_0| = \sqrt{(3-x-y)^2+(x-1)^2}[/tex]

I need to somehow find a relationship between these, and this is where I'm struggling. Any help would be appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex analysis limit

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**